When we owned a house, I had a 4x8 sheet of plywood for a gaming table (and of course the cats loved it).
I happened to have a large sheet of foam board that I started putting over games with several blocks strategically placed so as to not move the counters when the cats decided to sit on it. Worked like a charm.
Don’t have the house, plywood, nor cats now. :( Miss the cats.
I work for 3 cats, which is nice.