The device that plays the music (usually the host) needs an Apple Music subscription, so every pick plays as the full song. Friends who join on their own phones don't need anything.
Full songs play only on the host device or big screen. Players' phones don't need to sign in.
Opened this link from inside another app? Apple's sign-in only works in Safari itself. Tap the share button and choose Open in Safari, or type thatsmyjam.pplx.app into Safari.