A chess strategy is a decision process that suffices for all positions that can arise against any opposing play. i.e. it picks a move in every position that can arise when applying it.
I hope seeing the definition helps you.
To nit pick it needn't necessarily pick a move. It could pick a draw claim under the 50 move or triple repetition rules or the offer or acceptance of a draw or nothing at all if it's not your move.
These are moves in the general sense - choice of action when it is your turn,
It could also leave you free to pick from a selection of moves (as in a strategy that takes one of the best moves from Syzygy when available),
I said it picked a move. I didn't actually say it always picked the same move in a given position.
I would prefer:
A game strategy for a player is a function from the set of game positions with values that are (possibly empty) sets of actions for that player that are legal under the rules.
I am not sure why you want to permit an empty set. If it is your turn you need to do something!
Where a game position means simply a situation arising in a game.
As you are aware, it only needs to be the positions that can arise when the strategy is being used. Quite an important point, including practically - as eg 10^14 versus 10^20 positions for checkers (if I recall).
I might wonder how come you know the word "succinctly".
Then I remember that form doesn't = content. You're a fool.
Ahh, you've driven yourself back to the personal insults stage...the self-imposed break is usually not far behind...