Coming at it from an adventure gamer's perspective, I don't think of a puzzle like the type in Shivers or 7th Guest to be the same as a minigame. I think of "minigames" as being "little games" -- games where you're playing against an AI (artificial intelligence). I don't consider a puzzle to be the same as a game -- even an abstract puzzle that could exist outside of a computer game (like a puzzle box or slider). For as long as I've been playing games I've encountered abstract puzzles, and always considered them part of the game.
But people who play Hidden Object Games consider anything that isn't a variation of a hidden object search to be a "minigame." So we have this confusion because what is a puzzle for an adventure gamer is often a "minigame" for a HOG player. Maybe this is because HOG's started out as pure hidden object gameplay and didn't have the variety of puzzles found in adventure games.
As for personal preference, I don't enjoy having an interruption in an adventure game where I have to stop and play poker or 21 or Othello -- games where you have to play against an AI (or mini-AI). Even worse is having to stop and play whack-a-mole or use a shooting gallery or accomplish some other dexterity-related task -- which can be an impasse if there is no ability to skip it because no walkthrough can help you if you're too slow or too clumsy.
Interestingly enough, I don't think of chess puzzles as minigames, even though chess is a game. The reason is that you aren't playing an entire game of chess against an AI, and there's usually only one solution (or mirror image solution) to chess puzzles.
Do you like mini-games if they aren't timed? What do you think of timed mini-games within adventure games?
Timed is definitely worse. I have enough time stress as it is outside of games. The last thing I need is more.