Unfortunately I believe there's a no refunds policy with JRemote as there is one with JRiver Media Center.
I don't know if JRiver has a policy, but I know how the App Store works. Refunds and returns are always handled by the retailer, and that is not JRiver in this case, but Apple. If you buy some All Clad pans from William Sonoma, you don't call All Clad and ask for your money back. They didn't sell you the pans. You have to go back to the store. Same thing here. JRiver
can't give you your money back, even if they wanted to, because they don't
have your money, nor do they have access to your App Store account.
Apple does.
I do also agree that the App Store description couldn't have been more clear. In any case, I do also agree with this:
ActorCam, why not turn a negative into a positive?
How about you take up the 30 day trial evaluation period for Media Center proper and see how well it works with JRemote?
Media Center is better than iTunes in basically every conceivable way. Since you now have a $10 useless app, you might as well at least try the free trial of MC. If you don't like it, you're no worse off than you were before.