it's just the material used breaks down over time.
I have a computer mouse that I love that has some rubber grippies on the sides made of the same material. it starts off as a really rugged rubber then after a few years it's just broken down and becomes this sticky goop that comes off whenever you touch it. Never used any chemicals on it, it's just what happens. I have one on my home computer and one on my work computer and every few years I'm buying replacements... for a $30 mouse that's no big deal but I can see that being a problem with an arcade steering wheel.
the short answer is that these machines weren't mean to last this long so as long as the material had a nice finish through it's useful life, that was good enough.
your best option is to try to find a suitable replacement wheel that doesn't use the same material.