1 : to offer or represent to (as a person) a problem difficult to solve or a situation difficult to resolve : challenge mentally; also : to exert (as oneself) over such a problem or situation puzzled their wits to find a solution>
2 archaic : COMPLICATE, ENTANGLE
3 : to solve with difficulty or ingenuity <puzzle out an answer to a riddle>
I guess the games "challenge mentally", but so does every game (except sports games). WarioWare GBA is best described as a fast-paced action game, WarioWare GC is more of a party game, and Katamari Damacy is.. well, sort of a platform game, except you can't jump which takes most of the platforming out of it, but it's not a "puzzle" that is "difficult to solve". There are tons of adventure games that have elements more difficult to solve than Katamari Damacy.
If I were to guess, this is how Gamespot determines whether or not a game is a puzzle game:
- Surrealist graphics
- Minimalist storyline
- At least somewhat innovative gameplay
- OR it doesn't fit well with other genres
In my opinion, there are two types of puzzle games. In the first type, there are fixed levels that were made by the designers of the game and it is your job to solve them (like Bomberman I guess). I hate that type. The second type, which I like, is the one where there's random stuff (ie Tetris, Puyo Pop), and you have to figure out the best course of action. The second type are puzzle games just because there is usually an optimal placement and you are given a set amount of time to find it (like in Tetris, when you have X amount of time before the piece lands). The reason Tetris is a puzzle game and a racing game isn't is because in a racing game you have to follow a smooth line, not just make one good placement every so often.
It is narrow minded to call a game a "puzzle" game just because it has a style of gameplay you've never played before. Calling action-oriented games like WarioWare "puzzle" games is partly the reason people are scared of them. They don't like a game that's all about taxing the mind finding complex solutions, and if they don't read the review, all they see is "puzzle" in the genre field and move on.