When I was a kid I liked DOOM

There was a crappy nintendo game the angry video game nerd played that was doom reskinned as Noah on the ark. That's all I know off the top of my head.

Team fortress 2

Isn't overwatch kid friendly?

Splatoon is third person, but that's the closest I can think of

EDIT: I know some FPS's have settings that can take away the gore and curse words to make it more child friendly. And some games have paintball modes so no one is actually killing or dying

Overwatch, Paladins, TF2

Seems pretty cartoony to me. Though, I've never played it. Nor do I have children. My opinion isn't very useful in this particular situation.

All games are kid friendly. There is nothing in a game that will mentally screw up a child.

Off the top of my head, Nerf Arena Blast, an old kid friendly FPS that ran on the Unreal Engine 1. It's like Unreal Tournament (though using the same engine after all) but with Nerf guns. It is literally a "nerfed" experience when compared to UT.

This is very true.  Now excuse me while I go rip this guy's balls off with a pair of pliers...