That noise is the disc spinning.
Guilty Gear X is a blue-bottomed CD based game, a format which has problems with many PS2 consoles.
I just happened to buy Guilty Gear X the other day, and it does the same thing.
Funny thing is though, it will not read every single time. I have to set it into the disc bay in a certain way to prevent this from happening. (the label's picture facing me, basically)
While this issue comes from the many marks on the bottom of the disc, the loud noise does not.
It has to spin faster when this type of disc is read.
All of my CD based games sound like this, and the same goes for my brother's PS2.
Don't worry, your PS2 is fine.