I was mulling over potential options for future race picks and recently realized that a decent number of puzzle games would be viable candidates. While many would involve both luck and skill, they aren't too hard to pick up on:

Fire 'n Ice (NES) - Simple premise: Create ice blocks and extinguish fires. This would one where only doing the first few worlds would be most viable for those not familiar.

Kickle Cubicle (NES) - Top-down puzzle platformer. Freeze your enemies and fill in gaps to collect each levels items with a boss at the end of each world. The main game is easy to pick up, but can feel a bit long so doing 2 worlds at a time (out of 4) could be feasible.

Sailor Moon S: Kurukkurin (SNES) - Eliminate the same-color tiles to bring the three Talisman to the bottom of the screen with each character having a unique attack/skill. Super easy to pick up and a run against the CPU on Normal wouldn't take more than 2 parts even for a beginner.

I've done Let's Plays of all three and can answer any potential questions. Also willing to host a race of any of 'em if anyone's interested.