Why Salayatana is ommitted in this mode of Dependent Origination?

It is omitted because it is obvious the Lord Only Bhante Buddha did not teach DN 15.

DN 15 contradicts the True Dhamma in many ways, namely:

1. The sense spheres are omitted, which in AN 3.61 are included as a core teaching of the Buddha.

2. Consciousness is not the six types of consciousness.

3. Nama-rupa is the Brahmanistic nama-rupa of 'naming-forms' rather than the 'mentality-materiality' of 'feeling, perception, intention, contact, attention, earth, wind, fire & water'.

4. Birth is not the 'production' (abhinibbatti) of the view of 'beings' ('satta') based on the appearance (pātubhāvo) of the aggregates & seizure (paṭilābho) by the sense spheres.

5. Aging-&-death is not defined at all, let alone defined as the 'aging-&-death' of the self-identity of a 'being' ('satta').

6. Ignorance & sankhara are omitted.

'Salayatana' is probably omitted in this mode of Dependent Origination because this mode of Dependent Origination appears to be a later-day concoction for propagation to & conversion of Brahmans.

There have been a number of discussions on Sutta Central, which include Ajahn Sujato's agreement, that much of the DN, including DN 15, was probably composed for propagation to & conversion of Brahmans.

Thus, nama-rupa in DN 15 appears to have the Brahmanistic meaning. In other words, the 'salayatana', most specifically sense objects, are possibly included within 'form' ('rupa').

In Brahmanism, 'nama' was the naming of 'forms' (sense objects).

Nāmarūpa-vyākaraṇa (Sanskrit: नामरुपव्याकरण ), in Hindu philosophy, refers to the process of evolution of differentiation into names and forms i.e. to the unfolding of the primal state into the manifest world prior to which unfolding there was nothing that existed... In the Upanishads this term is used to indicate the self-willed manifestation of Brahman under visible and nameable aspects, to the said manifestation into the fictitious plurality of the phenomenal world...

The sage of the Chandogya Upanishad regarded the creation of the universe as a huge chest/egg from a Primeval Being existing as the undifferentiated whole, who alone existed without a second prior to the commencement of the process of creation which was the beginning of the differentiation of the undifferentiated. "The Primeval Being reflected, let me be many, let me produce; having bethought, thus to itself, it produced fire which produced water and from water was produced the Earth (food or matter)" (Chandogya Upanishad VI.ii.1-4). The doctrine of Trivritkarana, the prototype of the doctrine of Panchikarana that tells us how matter came unto existence originating from the primordial five subtle elements , belongs to this Upanishad. From the subtle elements were produced all gross elements, and all matter having names and forms that makes-up the entire universe.

Wikipedia

The doctrine of Paticcasamuppāda (Pāli) states that phenomena arise together in a mutually interdependent web of cause and effect. What the Buddha awakened to (Bodhi = ‘to awaken’) was the truth of dependent origination. This is the understanding that any phenomenon ‘exists’ only because of the ‘existence’ of other phenomena in an incredibly complex web of cause and effect. Buddha’s explanation of this in DN 15: The Great Discourse on Causation (Mahānidāna Sutta) - Dīgha Nikāya is exceptional compared to that of other suttas. What we are generally made to understand is that.. with Nāma-rūpa as condition, Salāyatana arises… with Salāyatana as condition, Sparśa/passa arises.

In DN15 Buddha says… With Nāma-rūpa as condition, Sparśa/passa arises. To understand this we have to read DN15 to the very end, and understand the explanation given in it about Nāma-rūpa. In DN15 we get to know two very special words:

Nama Kaaye patigha samphassa
Rupa Kaaye adhivacana-samphassa

“Nama” is the faculty through which the external world is understood. This makes discernment or our ability grasp and understand and naming of sense objects possible. For example we say that an Elephant is ‘Huge’; that an Ant is ‘Tiny’. This is Nama Kaaye patigha samphassa.

“Nama Kaaye patigha samphassa” is possible only if there is a “Rupa Kaaya”. Only if there is a species called “Ants” that we can name it as “Ant” and say that it is ‘tiny’. Only if there is a species called “Elephants” that we can name it as “Elephant” and say that it is ‘Huge/large’. This is “Nama Kaaye patigha samphassa”.

Then Buddha explains as to what “Rupa Kaaye adhivacana-samphassa“ is. When we converse that an Elephant is ‘Huge’, it is a perception (samjna/sanna) that we come to. Once we get to see an Elephant for real, we equate that given name & explanation to this Rupa-Kaya (Elephant). This is Rupa Kaaye adhivacana-samphassa. So whenever someone speaks of an Elephant, what comes to mind is this huge creature, and not an Ant. This is the ‘Passa’. For this to be, Vijñāna as condition, Nāmarūpa has to arise. But if Nama Kaaye patigha samphassa and Rupa Kaaye adhivacana-samphassa is not there, there cannot be any mode of communication, or any form of recognition.

Thus, there has to be some object in sight, for us to give it a name. If we have not developed a language to name things, there is no way that one can communicate what is in one’s mind, to another. In other words, this is With Nāma-rūpa as condition, Sparśa/passa arises. For this Sparśa/passa to arise, there were only two elements. One is the object in space (elephant/ant). The other is the perception (samjna/sanna) that came to mind. Remember that there was no ‘Salāyatana’ here. Only an agreed upon language of communication. Now in this present time and age we have added a whole heap of computer terms like ‘the mouse’, ‘ipad’, ‘facebook’ etc. These are Nama Kaaye patigha samphassa & Rupa Kaaye adhivacana-samphassa. There was no ‘Salāyatana’ here.

It looks like I am the only one who has given a clear direct answer to the OP. So I guess that I have earned the right to post another 'a bit' off topic answer, as it may shed some light to another fellow traveler of this road less traveled.

Why is there no ascension among Buddhist of the world? - Diliup Gabadamudalige / May 16, 2016

Why is there no ascension among Buddhists, the people following Buddha Dhamma all over the world except (maybe) among a few? The reason is that the pali thripitaka has been wrongly translated to English and then to Sinhala. Maghadi is language of sound. It is meant only to be SPOKEN. To write Maghadi, pali was invented. The people who translated the Dhamma did a WORD to WORD translation which cause the path to nibbana to be closed.

Simple example. Anichcha – has been wrongly translated to Anithya. Anithya is impermanence. Anichcha means a COMPLETELY DIFFERENT THING. It means that which cannot be maintained to ones liking. It is a THING OF THE MIND. Anithya on the other hand is a state of the Universe. Anithya does NOT always bring Dukkha or Duka or unhapiness or sadness ( or similar states).The death of someone in the next town does not make one unhappy. The death was cause by anithya but as one had no bond to that person no emotion,there is no sadness. BUT if one had a bond to that person in the next town, then that persons death will cause sadness becuase the bond is now broken. The bond – ichcha. You want that person to go on. Anichcha ALWAYS brings Dukha or Dukkha as one cannot control anything and keep them in the same state. Anichca is totally a state of the mind where as Anithya is a state of entropy. The way ichcha occurs are:

ichcha
patichcha
abhichcha
Nichcha
athta
uddachca or kukuchcha
patichcha
mahechca
laabichca
marichca
aththichch
vichikichca

The Maghadhi words of the Buddha, written correctly but wrongly translated, wrongly understood which led ALL except a few, astray. This itself is SANGHA BEDA.( This too is misunderstood as causing dissention or disharmony among two monks/priests etc.) But that is another discussion.

I'm not sure it is omitted: it's listed there as "consciousness":

From consciousness as a requisite condition comes name-and-form

I think that the ṣaḍāyatana are sometimes translated or understood as consciousness (which is listed in DN 15):

More specifically, according to this analysis, the six types of consciousness are eye-consciousness (that is, consciousness based on the eye), ear-consciousness, nose-consciousness, tongue-consciousness, body-consciousness and mind-consciousness

The word used in DN 15 is viññāṇa (the following quote is also from Wikipedia's Vijñāna article):

Hence, in this context, viññāṇa includes the following characteristics:

• viññāṇa arises as a result of the material sense bases (āyatana)
• there are six types of consciousness, each unique to one of the internal sense organs
• consciousness (viññāṇa) is separate (and arises) from mind (mano)
• here, consciousness cognizes or is aware of its specific sense base (including the mind and mind objects)
• viññāṇa is a prerequisite for the arising of craving (taṇhā)
• hence, for the vanquishing of suffering (dukkha), one should neither identify with nor attach to viññāṇa

I think that glossaries (e.g. here and here and here), and the so-called Viññana Sutta, say that although viññāṇa is a broad term it may include the six kinds of consciousness.

Or see this answer, which I think is saying that viññāṇa is used in two ways: technically as a specific aspect of mind, and colloquially to refer to several aggregates.

In case you want to read more (I'm sorry to post links instead of answering the question here, but they're long), Piya Tan of dharmafarer.org (for example) has written about this at some length.

Here is his analysis and translation of DN 15. The introduction starts with,

Moreover, its series of conditions omits three factors of the standard version: ignorance, volitional activities [saṅkhāra], and the 6 sense-bases. These omissions have led some scholars to suggest that the twelvefold formulation may be later augmentation of a shorter original; but such suggestions remain purely conjectural, misleading, and objectionable on doctrinal and textual grounds. All in all, omissions of the Mahānidāna Sutta are more than compensated for by its detailed explanations, interesting digressions, and supplementary sections.

And on page 156 (page 12 of the PDF):

In the next section of the sutta, instead of going on to the 6 senses and their respective contacts, as in the standard formula, the Buddha reverses his last statement and says: “With name-and-form, there is consciousness”. To prevent any misunderstanding, the Buddha then, introduces a remarkable passage unique to this Sutta: etc.

It doesn't seem to bother him that this sutta uses an other or a non-standard description. I don't know "why" it is slightly different but I find that unremarkable. It seems to me like asking, "Why is the house described as 'brown' here, whereas there it's described as 'made of stone'? Are they two different houses?" They're two descriptions of the same house.

Furthermore, here is Piya Tan's essay on the meaning and usage of vinnana (which I won't quote).

I'm not sure that it's necessary to put "6 sense bases" as a distinct layer between form and contact -- for example I think it makes as much sense to say that there are 6 types of contact.

For what it's worth, the 6 sense-spheres are omitted from the description of the five aggregates too.

The most detail version of Dependent Origination (DO) contains 24 points and extremely complicated like a web, which is called Conditional Relations or Patthana. The 12 link version is a simplification. Also there other simplified versions of which can can read more in Dependent Arising by Piya Tan.

If you take DO the most important part is ignorance -> ... contact -> sensations -> craving -> ... as this is the place you can break the cycle. If you look at Nutriment (ahara) this teachers this subset. If you look Suttas like Pahāna Sutta which essentially teachers a more simplified version of this: ignorance -> ... -> sensations -> craving -> ... or more inline with how it i presented: ... -> sensations -> craving | aversion | ignorance -> .... Also note when it says craving this includes aversion as aversion is a craving to part with.

Based on the audience and their inclination to understand, the Buddha is presenting accordingly.