Arkenbon

Terraria, for something crafty-buildy with combat and very cartoony/2d blood and gore. 1-8 players.

Don't Starve Together, survival crafting in a hand-drawn Tim Burton-esque style. 2-6 players.

Awesomenauts, 3v3 fast paced competitive game in the style of Saturday morning cartoons. 3-6 players.

Deep Rock Galactic, coop shooter where you play space dwarves and shoot bugs while doing missions together. Gore may be a bit strong for your liking, but it's very stylized and only against bugs and robots. 1-4 players.

Risk of Rain 2, shooter where you try and escape a planet together with lots of different ways to play. 1-4 players.

Age of Empires 2, old school fast-paced medieval strategy game modernized with new graphics and such. 1-8 players.

Valheim, viking survival crafty buildy game in which you explore and conquer a dangerous world together. 1-10 players.

Cassette Beasts, technically not multi-player yet but they're adding it as a free update January. It's a Pokémon-esque game where you'll all be trainers in the same overworld together capturing beasts and taking down challenges together. 1-8 players when it comes out.

All of these games are rated T for teen, but it sounds more like you're opposed to M rated violence and language than T levels. They're all also insular in that this friend group doesn't need to involve other people to play together and can either play with or against each other or the computer.