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The main aspect of this question seems to be just what exactly is Distributed Theory or Distributed Survival Theory. This is likely a reference to some anthropological/linguistic theories related to survival strategies making communication or language acquisition a survival requirement/advantage for groups which are forced, through lack of a particular resource, to reach out and have regular interactions with other communities.
The distributed strategy term seems confusing, but as often is the case further context may help clear this up. To understand the distributed strategy you have to have its counterpoint, which is the concept of localist strategy.
The book mentioned by @codeMonkey, The Horse, The Wheel, and Language by David Anthony, has an excellent discussion on pg 116 which I believe goes directly to the explanation we are looking for (emphasis mine).
In Jane Hill's study of the Papago Indians of Arizona, she found that communities living in rich, productive environments adopted a "localist" strategy in both their language and social relations. They spoke just one h*m*geneous, small-territory Papago dialect. But communities living in more arid environments knew many different dialects, and combined them in a variety of nonstandard ways. They adopted the "distributed" strategy, one that distributed alliances of various kinds, linguistic and economic, across a varied social and economic terrain. She proposed that arid, uncertain environments were natural "spread zones", where new languages and dialects would spread quickly between communities that relies on diverse social ties and redily picked up new dialects from an assorment of people. The Eurasian steppes had earlier been described by the linguist Johanna Nichols as the prototypical linguistic spread zone; Hill explained why.
I believe this is what your lecture is referring to.
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The author is probably trying to say "This language family is very successful, but please don't fall into the trap of thinking it's because of racist pseudo-science."
This is necessary because... people have used racist pseudo-science to explain the success of this language family in the past.
I'm not familiar with this course or "Distributed Survival Theory," but I suspect the author is taking pains to distance himself from some distasteful "theories."
Indo-Eurpoean is a very successful language family. Something like half of all living people speak an Indo-Eurpoean language. (English, German, Romance Languages, Hindi, Russian, etc.) When it was first discovered that these languages share a common root, the immediate question became "what is that root?" Linguists call this reconstructed root language Proto-Indo-European (PIE).
Around the same time that linguists first began reconstructing PIE, archeologists were discovering the Corded Ware culture. This is a kind of event horizon in European pre-history: a distinctive pottery style / material culture appeared in Eastern Europe, and rapidly advanced to the West. A similar material culture migration was eventually traced from Eastern Europe towards the Punjab, and from Vedic sources we had a name for the people bringing this material culture - Aryans.
This early work occurred in the late 1800s and early 1900s, and eventually the Nazi's heard of it, and decided the only logical answer to the question of "why was PIE/Corded Ware so widespread?" was an ancient race of super-conquerors, who they conveniently claimed as their own ancestors.
This "theory" has been thoroughly discredited - not the least of which through genetic studies that show the Corded Ware expansion was not unusually violent.
The course author appears to be proposing a theory that nomads are just particularly adept linguists, which I find... weak.
The generally accepted theory for the origin / success of PIE is the Kurgan Hypothesis. Basically, it is thought that the horse was first domesticated North of the Black Sea around 3,500 BC. The Proto-Indo-Europeans effectively exported their culture along side the horse - they had learned methods to train, breed, ride, and manage horses, and as they taught others these lessons, their language, values, etc. naturally spread as part of the interaction.
Because the horse was native to the steppe, and steppe-lands are not good farming lands, the PIE people were able to spread into otherwise unproductive lands in-between farming communities across Eurasia, allowing them to rapidly spread out - and co-exist with existing cultures. The sustained interaction between horse and chariot using PIE speakers and indigenous farming communities provided an effective window for cultural exchange, and the high-status associated with the new technology made PIE culture attractive.
Thus PIE culture effectively supplanted / merged with the existing cultures across Eurasia.
James Mallory is a big name in the field of PIE studies, and I recently read and enjoyed David Anthony's The Horse, Then Wheel, and Language as a layman.