The implication seems to be that the major labels get some fixed percentage of Spotify's revenues. I have no idea if this is true or not.
In addition to the percentage cut, they're also shareholders.
Besides, non-RIAA acts often use RIAA companies for catalog management, publishing and/or distribution. Even Radiohead was distributed by Sony.
An interesting graph illustrating how much an artist has to sell through various platforms (CD, spotify, itunes etc.): http://www.informationisbeautiful.net/2010/how-much-do-music...