Is there a game that doesn't rely on luck or skill?
How do you figure out who wins if there's no randomness (no luck) and no player decisions that can affect the game (no skill)?

If there's no skill, then that means players can't make meaningful decisions, i.e. ones where a better decision increases chances of winning. If there's no luck, they can't make meaningless ones either, like picking heads or tails on a coin flip.

That leaves games where the winner is pre-determined. For example, in Candyland, shuffling the cards determines the entire game. But then there's still luck, it's just that the entire game is one big coin flip.

So unless you believe in some concept of "fate", so that you can base the winner on who was "fated" to win, and declare that to not actually be luck, there can't be such a game. The player with the alphabetically first name wins? Use the players' names as seeds for a (deterministic) pseudo-random number generator, and use that to shuffle the deck in Candyland? Those still sound like luck to me; even though there's no luck in the actual "playing" of the game, one player was lucky enough to have been given the name that caused them to win.

Bottom line, anything where someone wins, there has to be a way they were determined to be the winner, and the common notions of "luck" and "skill" are such that one or both will always be involved.