I think it would eb nice made with a contrasting colour tape for the noughts and crosses board rather than white. Cut 4 pieces of herringbone tape (or you could probably use ribbon but its not as hard wearing) pin them on to the towel and stitch along all of the edges - I would probably do one at a time rather than trying to sew the whole thing in one go. Use shells or pebbles or driftwood for the counters.
you never know - if you take one of these to the beach with the children you might even get to sit down and read more than 3 words of a book!!!!