Sure, but how is that relevant for my argument? Kids and adults enjoy chess and checkers, both should have access to public chessboards, slides and swings are for the most part only enjoyed by and only safe for kids.
There are lots of chess boards outside of playgrounds. They are generally occupied by adults. I think the point of putting the table inside the playground was specifically to enable kids to use it.
Amending the sign to read something like "no adults, unless playing or watching chess, but not if a child has been waiting to play, except ..." would get complicated fast. Just go to a different park already.