Is Chögyal Namkhai Norbu correct when he says our life is unreal and that Buddha taught that life is just like a dream?

I doubt a Buddha would ever teach life is like a dream. Such a teaching may cause people to act in life nihilistically with negligence, such as Tibetan gurus who engage in sexual misconduct.

In MN 54, the Buddha taught sensual pleasures are like a dream. In Thig 14.1, Subha the nun said being beguiled by a woman painted with make-up is like a dream.

But in AN 3.136, the Buddha taught conditioned things have a fixed quality, in that they are impermanent, unsatisfactory & not-self. Seeing all conditioned things are unsatisfactory is not like a "dream" because dreams can imagine things to be pleasurable or satisfactory.

Also, Nibbana is an experience of those who have lived the Holy Life. In MN 140, the Buddha said Nibbana was "undeceptive" and "true", which, again, is not a "dream".

In MN 29 & MN 30, the Buddha taught the essence of the Holy Life is the unshakeable freedom of mind. This Holy Life is not a dream because Nibbana is permanent and undeceptive.

But dreams are real—when you are dreaming, you are really dreaming. But their contents are not (always) true. They are like a movie, which is something you can watch, but the movie’s contents—the actors, and the action, and even often the setting—are not true. This comparison just like is not saying two things are identical, it’s comparing one thing—our life in this case—to an evident particular characteristic of the thing it’s being compared to—a dream in this case. A dream is illusory, but you really dreamed it, and it is this characteristic of being illusory that our life is being compared to. But you are truly living. It’s just that there is something illusory about the actors—they seem like they are truly separate beings, but they have no independent self nature; and there is something illusory about the action—it seems as if there is something happening to you, but your intrinsic awareness (he was teaching the view of Tibetan Dzogchen) is not changed in any way by what is happening; and even the location is illusory—every quality you believe is a quality of the world around you is something that is of you, and not otherwise (for example, you see red, but what you believe is red is just how your eyes perceive what is there).

So our lives are real—we are truly living—but everything that happens in them is illusory in some way. That’s what Chögyal Namkhai said. You only thought he said your life is unreal. He said (that Buddha said) that it is like a dream, and the salient characteristic of a dream is that its contents are illusions—seemingly real while you are really dreaming, but then discovered to have been illusory.

Addendum (to answer Yeshe Tenley's request for a definition in the comments below):

To be real, something must be non-contingent, necessary, simple, and evidenced.

Non-contingent, means that it cannot be dependent on anything else in any way. It can’t be brought into being, caused, or created, for example, and it certainly can’t depend on you experiencing it for its reality.

Necessary, means what it says. What is real must be necessary—like a motor in a car, or a charge in its battery—or nothing works. What is real cannot be an option that one can take or leave, something gaudy to set our car apart from those of others.

Simple, means it is not a collection of parts; it is not a union of aspects—it is not structured in any way. The reason for this is that if a thing isn’t simple then it depends on something else to cause it, or make it, to be, and so it is contingent. Therefore, what is real is necessarily non-dual.

And finally, what is real must be evidenced. If a thing isn’t directly evidenced—since I am asserting that it doesn’t exist, i.e., it can’t be experienced—if it is just inferred, hypostatized, or hypothesized, than it’s not real.

When I say that something exists, or I talk about existence, I mean that imperience is happening, could happen, or did happen. And that is all I am saying, having already seen that the contents of experience were ephemeral at best and certainly lacked any inherent self-existence, how can I assert that any of it is real?

Please note, imperience is a technical word for me; we imperience a dream, but experience its content.

This is taken from my article, "Reality and Existence" and the longer subject of what I mean by imperience and experience is another article "Understanding Experience" which is very relevant to this question, but a decently long read.

Fwiw Buddha compared sensuality to a dream as well. I don't think this tenet of the Dhamma is central to it because it is still open to be interpreted in favor of an eternal & underlying consciousness doing the dreaming.

As i see it, the latter point not being thus interpreted is the central tenet and what separates the Dhamma from eternalism.

Also this support from Dhp

One who looks upon the world as a bubble and a mirage, him the King of Death sees not.
Dhp 170

The point is that when we look out into the world and we see (say) a tree, a dog, a car, a white cloud, or whatever you like, what we're actually perceiving is color, shading, texture, apparent movement... We receive this great wash of ambiguous sensation, and in our heads we establish boundaries, conjure up structures and patterns, intuit relationships, and fit these sensations into concepts, discarding most of the sensations that got us there. We then treat these conceptual objects as though they were part and parcel of the real world, instead of fabrications we impose on the real world after-the-fact.

When we sleep these concepts sometimes float free of any referent and appear to us as dreams, but seeing a dog running in a dream and seeing a dog running in a field is merely a matter of degree. Both have that 'dream-like' quality of a conceptualization that is at best loosely connected to anything material.

The Pali suttas are almost the same as Mahayana agamas in Sanskrit, and so would be on-topic as Mahayana-relevant content.

From Dona Sutta, the Buddha calls himself "awakened":

"Just like a red, blue, or white lotus — born in the water, grown in the water, rising up above the water — stands unsmeared by the water, in the same way I — born in the world, grown in the world, having overcome the world — live unsmeared by the world. Remember me, brahman, as 'awakened.'

This means he has awakened from a dream of course.

Awakening from the dream does not mean that the world is a dream or that the world is unreal.

It's because the dreamer (the self) is unreal, as the Buddha taught that all phenomena is not self (sabbe dhamma anatta - Dhp 279).

Upon waking from the dream, the dreamer disappears in this case. Also all reification/ objectification-classification/ papanca arising from the self - non-self duality is the dream that disappears.

The chair however doesn't disappear and the Buddha can still sit on it.

From Vina Sutta:

"In the same way, a monk investigates form, however far form may go. He investigates feeling... perception... fabrications... consciousness, however far consciousness may go. As he is investigating form... feeling... perception... fabrications... consciousness, however far consciousness may go, any thoughts of 'me' or 'mine' or 'I am' do not occur to him."

From Tuvataka Sutta:

"I ask the kinsman of the Sun, the great seer,
about seclusion & the state of peace.
Seeing in what way is a monk unbound,
clinging to nothing in the world?"
"He should put an entire stop
to the root of objectification-classifications:
'I am the thinker.'

The translator commented:

On objectification-classifications and their role in leading to conflict, see Sn 4.11 and the introduction to MN 18. The perception, "I am the thinker" lies at the root of these classifications in that it reads into the immediate present a set of distinctions — I/not-I; being/not-being; thinker/thought; identity/non-identity — that then can proliferate into mental and physical conflict. The conceit inherent in this perception thus forms a fetter on the mind. To become unbound, one must learn to examine these distinctions — which we all take for granted — to see that they are simply assumptions that are not inherent in experience, and that we would be better off to be able to drop them.