It has to do with the laser being worn out. This method slows the CD motor down, helping the burned game be read. People have done it by pressing firmly on the lid, which puts pressure on the top of the spindle, causing motor strain. Some people put the whole unit on its side. Other methods include adding two CDs to the spindle, obviously with the data one on the bottom, to add the strain.

There is also a 3D-printed weight disk people use at https://www.thingiverse.com/thing:4838168 .

How does a worn out laser/motor affect how a burned game is read compared to the genuine discs? I don't follow.

I think burned discs are of lower quality generally, so that's the distinction.

Presumably the laser is dimmer and less efficient and therefore giving it more time to scan and read each bit compensates for this.