That's normal. It just means the game is stored on a CD instead of a DVD.
I'm not too sure about 2nd gen PS2's but from personal experience, PS2's have trouble reading CD's after a while. An old remedy for this was to put two pieces of tape (or a CD label) on the disc to weigh it down, since CD's are lighter than DVDs. Sounds like the previous owner of your copy botched the CD label application, making the disc unstable (hence the noise).
The only consequence to your PS2 is it might damage the lens. My first PS2 started making loud noises when loading a disc, before it finally stopped reading them altogether.