Hmm... hard to answer. We don't *really* know why the Indo-European groups succeeded as they did. There's a theory that they were relatively successful in Northern Europe, because they cleared the forests for use in pastoralism in a bigger way than the preceding agriculturalists, who might have concentrated more on finding small areas of fertile land and raising crops. Though even the predecessor cultures were not strictly pure agriculturalists (Funnel Beaker culture for instance, much of whose cultural products seem adopted by probably Indo-European speaking Corded Ware horizon, used a lot of domestic animals and were quite mobile).
But it seems quite likely to me as well that they were simply more mobile than most other groups, and so ended up amassing quite a large territory that way, and then assimilating or replacing other peoples, depending on population density. Where less mobile cultures were not as expansive or migratory in the same way.
In particular this could be what led to them being poised to become important in down phases of early civilizations (Indus Valley for instance, where not much evidence of Aryan invasion, but the fall of the culture may have allowed extensive migrations to take place).
Much of the stuff about distinctive Indo-European religion and social structure beyond high mobility I take with a pinch of salt.
It really depends on how you butterfly out the Indo-European cultures. I think the only couple things that seem really likely to me are:
- Languages would likely have been more deeply diverged and hard to learn over a large zone, at least until major empires came and homogenized regions, and so transmission of some ideas might be slower (or people might just be more linguistically capable).
- I'd guess that people living in Europe may have followed paths of being more intensive in small regions and less extensive in their agricultural systems, and with more density, earlier, perhaps more proto-urbanism and civilization about well before in our time line... but on the other hand, maybe not, if extensive, low density systems in much of European pre-history post-IE migrations were primarily ecologically determined.
Re: the European lactose tolerance variant, it seems to be absent in the early and presumed Indo-European culture of the Yamnaya, Afanasievo and Poltavka, but then shows up later with cultures who seem from genetics to have absorbed people from the Neolithic cultures in Europe. So may equally have existed in the early PIE people, or come from non-PIE Neolithic cultures west of the Pontic-Caspian steppe, who tend to have some extensive evidence of milking themselves.