Shooter games? Counter strike can be played offline with bots and it’s free. Aimlabs is made specifically to improve aim, also free. Faster paced strategy games like Dota 2 also requires accuracy to click on monsters and enemies and can be played offline with bots and it’s free.

More story-oriented games of course could also work. StarCraft, company of heroes, command and conquer, age of empires, etc. For shooters there’s tons, but many have gore…you can try portal or slime rancher but I was playing doom and Wolfenstein and stuff like that when I was like 10 and whatever as did many of us…but well…not here to give parenting advice, shouldn’t listen to me.