What causes certain PlayStation 2 game disks to spin quicker than others whilst in the drive?

There are 2 possibilities

Location of Data:

CDs and DVDs from this period were usually still read at a constant linear rate. This means that at the read head the CD/DVD must travel over it at a constant speed. Data on a CD/DVD has the same size per bit on the inside and outside, meaning that there is more data per revolution on the outside of the disc. Therefore, to provide a constant speed of data input over the reading head, the disc spins slower when reading the outside.

(Later, faster drives switch to a constant angular rate which meant they always spin at the same speed, and the data input speed changes depending on which part of the disk is being read)

Because of this, if the game needs to constantly read data that is near the outside of the disk, it will spin slower. This would explain different rotational speed for a single disk

Read Speed:

CDs and DVDs are read at different speeds

For the Playstation2 these are the specs:

24x speed CD-ROM [3.6 MB/s], 4x speed DVD-ROM [5.28 MB/s]

24x speed CD-ROM can typically spin at 5k to 12k rpm

4x speed DVD can typically spin at 2.2k to 6k rpm

This is probably why you noticed the CD ones spinning faster

Source 1 Source 2 PS2 Spec Drive Speed Source