Why are 88×31s that size, it's a bit of an odd size to pick? When you Google that question people often mention Geocities requiring a link back to their main page, with the button asset being 88×31, but someone must've still chosen it.
The only technical thing that might be an answer I can think of is that 88×31×24 bits is extremely close to 8 KiB – when limited to 24-bit colour the only closer value is 2 pixels larger e.g. 91×30 or 78×35 – however as I mentioned this is assuming full 24-bit colour (and also no compression), and at this time most images would've been GIFs right, which use indexed colour. I can't actually think of any reason that an image / animation frame would be limited to 8 KiB, so this is probably just a coincidence.
Perhaps it really was just a random artistic decision? Still don't know why they chose that over a more round size or aspect ratio, but oh well.