Short answer: They're not.

[citation needed]

I'm pretty sure there's a legal loophole occurring here. All of the music on Grooveshark.com is uploaded by the users and Grooveshark is not responsible for the content. If the song is copyright it's user who broke the law, not Grooveshark. It's a similar concept to copyright videos on Youtube.

You're talking about DMCA safe harbor provisions, which would only apply if Grooveshark promptly took down content when requested by copyright owners. Further, Grooveshark isn't even claiming the service is for "user generated music". (YouTube is different on both those points.)

The only music I’ve seen taken down was from the Beatles.

and Pink Floyd

can't find Smashing Pumpkins on there either

Glad to see that I'm not the only one. I was very confused, I was in a weird mood and was looking for both Pink Floyd and Smashing Pumpkins, but couldn't find either of them. Now I know...

Oh yeah, couldn’t find Gish on there the other day. Good point.

I can't imagine that this will hold up, in the long run. Torrent sites get taken down without even hosting actual content, the way that Grooveshark does. So wouldn't it simply be a matter of time before they either cut some sort of deal with the RIAA, or get shutdown completely?

It worked for YouTube, it its heyday it was all illegal content. They've already got a deal with EMI and prolly Universal soon (they're suing Grooveshark,but that's the same way they got the EMI liscense) Also they supposedly put a chunk of cash in an escrow account for when the labels come knocking.