Thats basically what is wrong with mine. I cleaned it with a cleaning disk and it still won't read DVD Games. This is very frustrating because that's the main reason I have this computer.
I don't think a cleaning disk is that effective. You should get a q-tip and some rubbing alchol and work on it directly.
I have published thousands of cd rom disks full of shareware and the burners where beaten so heavily I had to clean the lenses frequently.
That doesn't mean it will fix it but easier than replacing the dvd.
You will have to try another dvd.. or at least check your game disks in another computer.