I think the wording would be better as:
Whenever a player plays an instant or sorcery card, each other player may pay

. Each player that does may copy that card and play the copy without paying its mana cost.
***
That wording avoids ugly references to the stack and follows the patern laid out by Isochron Scepter. It still has some weird effects, by letting people cast sorceries on other people's turns. What happens when somebody casts Relentless Assault?