You are using the wrong kind of alcohol with rubbing alcohol. Rubbing alcohol is isopropyl alcohol. Your best bet is ethanol. Guess what kind that is! Try some vodka or something stronger if you have it. It probably won't remove all of it but it may remove some. I am guessing the mat is porous and the ink has soaked in.
I keep cheap vodka around to use for a lot of things and none of them are drinking. I work in a lab and we write on everything with Sharpies. We remove it with ethanol, but our ethanol is 95%. Everclear is as close as you will come to that!