Do smart people like video games? If so, what type of games do they like?
Video games are no longer a niche interest that is derided for being enjoyed only by sheltered nerds (speaking as a nerd who remembers when games were considered nerdy).
So your question is basically like asking "Do smart people read books", or "Do smart people watch any films". Games are now a mainstream medium of artistic expression that's generates billions a year. It's statistically unlikely that no smart people play them. Which ones they play however would depend entirely on what they want to get out of them, since as with other mediums, there are many genres that appeal to different people.