Does Von Neumann's Minimax Theorem concluding that it doesn't matter which player moves first (when moving means submitting a probability distribution whose realizations take place after both moves are submitted) apply to zero-sum games only if they consist of a single move from each player, or does it also apply to zero-sum games which have several alternating moves (the type of game ordinarily solved by backward induction)?
If the latter is correct, then why does the theorem not imply that neither white nor black has an edge in Chess?
If the former , then why does the theorem appear when players use multiplicative weights to play zero-sum games over a sequence of periods in online learning models?
It's both. Well, it applies directly to 2-player zero-sum games in normal form (i.e. a matrix game, i.e. each player simultaneously picks a single move).
However, an extensive-form game (EFG, a formalism for sequential games) can be converted into an equivalent normal-form game (see: Kuhn's theorem), by creating a matrix game where every pure strategy is an action of the matrix game.
Thus, the minimax theorem applies to sequential games as well, but in the space of pure strategies -- this means that in chess, it doesn't matter who chooses their strategy first (obviously, since if each player can choose their strategy, they should just choose to play The Optimal Strategy).
Details:
A pure behavioral strategy for a game like chess is a function from a board state to an action. So when each player chooses their strategy before starting a game of chess, it means that each player commits to the move that they would play, for every possible state in the game of chess.