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With "War" it's indeed possible to win, though.

The only winning move is not to play?

War is also entirely deterministic and contains no choices, so some don't consider it a game

Hmm! Because once the cards are shuffled everything is a fixed series of events?

Would Snakes and Ladders be the same then if we replaced a die with a randomized deck of cards of the numbers 1-6? And in that sense: any “game” that’s purely random is also not a game then?

Agree but I think these things can be considered games in the sense that it gives younger kids practice in following rules and interacting within a group. Also is an activity for them to spend time and there is a concept of 'winning' even if the participants cannot impact that.