I haven't backed up any PS2 games but I am sure that DVDFAB Platinum will, if you look at a few threads here you will find your answer and how to do it. If you go back a couple of pages you will find your answer and what you need.
Also, older ps2 games are CD, most newer titles are DVD's, so you need to use different programs for both.
It is not that hard to do, & remember to use good grade media such as Verbatim or Taiyo Yuden!
Ditto! I have not used DVD FAB, but have used DVD Decrypter for DVD games, & Slysoft for CD games. I only had a few CD games to backup, so the trial period worked for me.
There are plenty of threads on here for instruction on how to do it, use the search!
Good luck, katzz