It would have to be games for which AI could not be programmed so easily.
Once a game would have AI programmed for them anyway we would have to drop it.
So basically we would be adding new games every once in while.
What kind of games can you think of that would be hard to program a bot for? Chess? I could have a bot up and running for any game you can think of within half an hour
Obviously you cannot use game like Chess that have been around for a long time. Because there are plenty of AI programs already developed for them.
So I would introduce completely new abstract games with deep branching factors.
For example the game "Nymbat" that I have developed:
http://www.cjgames.com/index.php?page=nymbatI don't think you can program a bot within 30 minutes to beat me at Nymbat. Are you willing to make a bet on that?
Also, you could randomly challenge a player with catpchas to check if there is a human actually playing a game. This would at least discourage bots running automatically without a human attending.
Similarly, we could also make some completely new retro-style video games.