I was thinking about playing High on Life shortly after the release but I've seen a few reviews that depict the game (or maybe just the jokes) as so-so.
I think Portal 2 is probably one of my favorite games that has a lot of humor at it's core. But I can't say I've played a ton of games where that is a front-and-centre core element. I know there are some cult classics out there that I haven't gotten around to playing yet like Conker's Bad Fur Day and Psychonauts.
It also doesn't need to be an entire game. The Hotline Miami 2 workshop content GARFIELD CAMPAIGN made me laugh.
Edit: Bonus points/extra challenge if it's not on PC. While I do game almost exclusively on PC I would be curious to hear what's out there for handhelds like GBC, PS Vita, 3DS, PS2, PSX, and so on.
When it comes to “classic” comedy, then Hi-Fi Rush is one of the highlights in recent times. Not only are there a lot of jokes in the dialogue that landed for me, all the cutscenes are also loaded with perfectly timed visual gags. Lots of humour hidden in the environment as well.
Other than that, any “serious” game that has a wonky physics engine can accidentally be pretty funny on accident. Slinging around corpses in Dark Souls 1 for example.