I quite liked disarming chests in Wizardry 7... it's a combination of skill-based die rolls and pattern-matching when you try to guess the type of trap. Unfortunately it gets impossibly difficult for the lategame chests like the gorrors - you have to savescum for chest content and party survival.
Lots of minigames can be found in Nethack and other roguelikes: praying at altars, using potions of blessed water (uncursing/blessing inventory, especially scrolls). Making blank scrolls by dipping them in water, then using ink to write known scrolls. Digging. Wishing. Genociding. Strategic inventory stash management. And the whole identification minigame.
Lots of minigames can be found in Nethack and other roguelikes: praying at altars, using potions of blessed water (uncursing/blessing inventory, especially scrolls). Making blank scrolls by dipping them in water, then using ink to write known scrolls. Digging. Wishing. Genociding. Strategic inventory stash management. And the whole identification minigame.