Hmm... I think a party is a different case. If it is in your home, it could be regarded as private, so that is different.
As for a public gathering but not to make any money, at my church we pay a licensing fee per year for the use of music. But whether that is to sing the songs or to use the written music to play them (or both?), I am not sure. However, if it is for simply "playing" the songs, you could argue that a church doesn't do it to make any money either, yet they still pay royalties.
Possibly gyms have an arrangement for paying yearly licensing fees. I have no idea. But I'm interested to know how it works.