It was my understanding that DVD X Copy was for movies. So the program is going to try and look for Video_TS and Audio_TS folders, VOB files and the like. Nothing in there would even remotely translate to a PS2 game. Plus, DVD X Copy isn't readily supported anymore anyway, so its become equally as useless for movies due to the encryption standards changing.
Just take a look around this site, research things like DVD Decrypter, Alcohol 120%, and search out some of the game titles in our search function to see if anyone has had any discussions on it. Chances are, there will be, for the most someone telling you exactly what you need to do to copy it.
Keep in mind though, you will need either a swap magic or modchip to play these games once backed up. Thats only half the procedure.