Not a minigame, but Maniac Mansion being within The Day of the Tentacle is probably my fav.
The full 4K version of Timesplitters 2 inside Homefront: The Revolution, but you have to play something like 75% of Homefront to reach it. I’ll reach it one of these days.
Caravan from Fallout: New Vegas has a notoriously bad tutorial, but is easy enough to grasp and fun as an early-game money source. Would have benefited from a Gwent-style sidequest chain.
The minigames in shenmue/yakuza. They are literally full games.
Probably not what you are asking for, but the character creation process in the Traveller ttRPG is a great mini game. You basically take a person from 18 to however old you want, and their life path is dictated by your choices and random dice outcomes. It’s a lot of fun. You can end up with a retired admiral, a prisoner or criminal, psionic, etc. Going through this process with a table of friends let’s you build in rich fun connections along the way. The actual RPG then starts with mature, connected characters with a history, instead of 4 randos meeting in a tavern. In the classic Traveller you can even die in character creation. Current iterations removed the death component but you can be maimed from accidents in your career and start the game with a mountain of medical debt.
Playing Receiver in Receiver 2 was a fun surprise.
Geometry Wars in Project Gotham Racing 2.
The Chao racing from Sonic Adventure on the dream cast. You could take the memory card out and use it as a tamagotchi to care for the little guy and make it train so it gets faster and stronger in the real game.
It got no better than that.
Pretty much every minigame in Majora’s Mask is making you forget the world is ending
Ratchet and Clank: Up Your Arsenal had a side scrolling Captain Quark game that was quite good
Treedude in superhot
And… Umm
Mario party
I thought of another one. There is a minigame in Xenoblade Chronicles 2 called Tiger! Tiger that is great. it is basically an arcade game where getting certain scores gives you credits that can be redeemed for upgrades for some characters. The minigame is randomized and has three different difficulty tiers and is overall really well done.
Not sure if it will count, but the Ancient Cave in Lufia 2 (SNES) was a game in and of itself. It was basically a roguelike dungeon. 100 random floors, it reverts you to level 1 and there were rare special items you could sometimes find in runs that could be brought back in. Beating the Ancient Cave is much, much harder and more rewarding than beating the game itself (storyline aside).
Demontower, found within Night in the Woods. That could easily be a standalone short game
The hunting game in Oregon Trail.
