Option 1 -> "despite" requires a noun phrase, not a clause, so "despite the game is being played" is grammatically incorrect.
Option 2 -> "during" is a preposition that needs a noun (like "during the game"), not a complete clause with a verb.
Option 3 -> "while" is a conjunction meaning "during the time that" and correctly connects two clauses, fitting both grammatically and contextually.
Option 4 -> "much as" means "although" and creates an illogical meaning in this context.
Hence, Option 3: while -> This conjunction appropriately indicates that players cannot leave simultaneously with the game being played, establishing the correct temporal relationship between the two actions -> correct