It depends if the charges are processed by the hotel, or if the facility is a separate business with its own merchant account. Both arrangements are possible. You could ask the gym how the charges are processed, but the only way to know for certain is to try it.
I shown on my statement as
HILTON KUWAIT RESORT SAFAT KUWAIT
Do you think that would qualify as 'spend'?
If so, do you think it's worth it? Probably worth 6k points to me this year, plus any sign up bonuses.
Andrew