Ritz-Carlton Rewards members can earn and redeem their points at The Cosmopolitan. They can also receive their Elite benefits there. As a member of the Autograph Collection, the hotel is part of Marriott Rewards, which is a partner of The Ritz-Carlton Rewards program.
Adding to the confusion slightly, there's the Cosmo's own rewards program called Identity. This program gives you points for all the activity you do on-site at the hotel from gambling to dining to spa-ing and shopping. Those points are then redeemable to use back on the property (not at any other Marriott hotel.)
Confusing? It sure is so you should spend some time reviewing all the programs before you get to The Cosmo to see which one is best for you.