If you use the word game 'minigame' very liberally you can call a lot of mechanisms as 'minigames'. Like crafting in Diablo II.
You mentioned Playstation - maybe our view is different because I'm a PC gamer. And yes, most of the games I like are
older than 20 years.
Worms, Diablo I & II, Heroes of Might and Magic II-III-IV, Baldur's Gate I-II, Deus Ex, System Shock II, Planescape: Torment,
Doom I-II, Duke Nukem 3d, Age of Wonders, Master of Magic, Master of Orion II, Civilization series, Age of Empires, Blood,
Quake I-III, Re-Volt, Need For Speed 1-5, Unreal/UT, Max Payne 1-2, Warcraft 1-3, Starcraft etc.etc.etc.
None of them contain minigames. Although you may argue that some of them have such element which may be considered
as a minigame. The first time I think I encountered a minigame was when I played a Warcraft 3 mod around 2003.
Minigames can be fun, though I kinda feel that in many cases they are there only because A) they are popular B) they are
filler to increase play time. If used incorrectly it is a chore and breaks immersion. For me a good example (for a good usage)
was Witcher 1's dice poker. It was kinda fun, and a very good (though pretty short) music track. Bad examples where you
are just forced to get resources by boring minigames needed for advancement. TL;DR when they turn into chores.