I bet it was left, since you found it on Saturday, and some tourists consider them as disposable. I believe it now belongs to you. ;-) I have enough "lost" boogie boards in my garage to start a store. Having to leave all the newly "lost" ones (washing up at Grayton or floating in the lake) at the garbage can.
Can't imagine someone trying to claim one. I see the same patterns repeatedly in the surf when I walk. I leave the fiberglass ones as they are more expensive and not so likely disposable. The foam boards are many times broken when picked and obviously discarded