Do you know what the top of your table is made from? It looks like wood, although the grain pattern is quite unusual? The top of the table seems to be veneered?
Magic erasers are mildly abrasive and have to be used wet - I definitely wouldn’t use them on wood, unless I knew it had a polyurethane lacquer that was waterproof.
I suspect that dye from the bar mat has discoloured the table. (There was probably some horrible small print somewhere that advised not to put it on a light surface in case of colour transfer.)
I’m normally a fan of DIY repairs, but in this case, I think you need professional advice. I suspect that this is going to need sanding and refinishing, and you would have to be very careful sanding it as the top layer will be very thin. Given the cost of the table, I’m not sure I’d want to chance it.