AnyDVD only works for DVD Movies not games. The fact is Sony mostly rely on protection that can not be burned. That is why you need a mod chip to play your backups.
The fact is for nearly all PS2 games can be backed up with just about any DVD copy software. Exceptions are things like Mercenaries and GT4.
As quoted from the Slysoft web site:-
AnyDVD works in the background to automatically remove the copy protection of a DVD movie as soon as it's inserted into the drive, allowing you then to backup the movie using a DVD backup tool such as CloneDVD and CloneDVD mobile. You can also remove the RPC region code, thereby making the movie region free and viewable on any DVD player and with any DVD player software.