It'll depend on how much data is being reported back. For some games where users are asked to make certain moral choices, I figure you can infer a lot about someone by analyzing those choices.

Imagine if games like Mass Effect phoned home about the choices you took. You can build up a pretty complete psychological profile of someone based on their gameplay.

I really doubt that, honestly. You have no idea if those models are correct without comparing it to real personality of an actual person.

If anything, you'll be dumped into big buckets like "buys lots of cosmetic items", "usually makes good choices first", "likes to try breaking aspects of games", etc