There are plenty of competitive programming sites where you can grind rating just like you would for MMR rating in video games.

For example CodeForces, AtCoder, TopCoder, and even LeetCode have rated contests

Thanks ghj.

I was aware of top coder/leet code, though hadn't heard of code forces/at coder.

For me the adventure game give a bit more concept linkage. Take Monkey Island, I can remember how to reply to many of the sword fighting insults, or what was needed to get pieces of eight via the cannon at the circus. There's something to be said for linking problems via a memorable story, giving examples and meaning from multiple angles helps retain the content over the dryness of problem prompt/quick solve.

For me, codeforces is fun the same way chess is fun. Yeah, the mechanics look dry on the surface, but lots of variation under the surface, and lots of chances to link concepts by having an aha moment during the contest or afterwards in analysis.

Usually when you try to combine education with gaming, the result is something that's not very educational and not very fun.

It can be done, see Dragonbox Elements or Dragonbox Algebra.