Since it's "You can play this card only if there is any Stadium card in play", that's the requirement for playing the card. Everything in the second portion you "do as much as you can", meaning that you attempt to discard it and fail, but that doesn't prevent the rest of the card form resolving. So if there is a Thunder Mountain <> Stadium in play, for example, you could play Bonnie every turn and keep using Zygarde-GX's GX attack each turn (assuming you had sufficient Bonnies).You can play this card only if there is any Stadium card in play.
Discard that Stadium card. During this turn, your Zygarde-GX can use its GX attack even if you have used your GX attack.