Keep in mind that list of unsupported games only applies to Playstation 2s with a model of SCPH-75001. From what I can see, that is some of the slimline PS2s only, due to a change in the chips used onboard. The PS2 will hand control over to the I/O processor when a PS1 game is inserted, as the I/O processor is the same as the PS1 main processor.

Nintendo did the same trick with the Game Boy Advance. They used the older Game Boy Color processor as some minor chip, until a Game Boy game was inserted.