Many mentally challenging activities I'll start spontaneously, but it's typically small ones with direct, achievable goals, like write a little scraper in a new language or reverse engineer a single mechanism of an application.
I only have a few times a week when I have downtime that I feel like I can pick something off a list. The rest of my downtime I want something to do - and that's where games come in - and I'm quite glad for them, because without them I'd spend much more time watching TV, reading junk political threads on reddit, etc.