Yes. That looks like a feasible solution to get those tables corrected. And, could be possible that the ones installing these tables didn't know about the chess boards or missed to take care of it.
A New Park Table
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I opened the second image in a new window (right click the image) so it would be larger, and I could see that the tables are bolted to the bricks underneath. Someone could simply unscrew the nuts on the bolts, turn the tables 90 degrees, and rebolt them. The tables would now have the correct orientation with the dark square in the left-hand corner. Seems an easy fix.