i have found very similar broken tiles on beaches in Greece and Turkey, they are not "modern" in the sense of the last 50 years or so but i was never sure either.
The fact that although a soft material, they are very surf tossed and rounded makes me think at least 100 + years old. But that layered manufacturing process is interesting too. These pieces could easily be tossed scraps from a "remodel" of 100 years ago...after all if you live by the sea, where else are you going to pitch your garbage?