Will this floor tile break?
Pry that tile up, it sounds loose on that corner - i.e. not only unsupported, but some of the thinset in contact with the tile did not adhere.

That looks like unglazed clay tile (aka mexican clay tile), which you must moisten on the bottom to get it to adhere well.  If you don't, the tile sucks the water out of the thinset before the thinset can bond, and you get what you have with that "klonking" tile.

If it was just voids at the corners, you could just "pipe" some more thinset under the tile with a pastry bag, but after watching that video, I would pry up that tile.  Hopefully you have some spares.