Some people like things just so, even if "just so" seems a little out of place. There's a method to their madness.
This cat is no different.
A human "fixes" a chipped bit of tile, nudging it back into place. And it looks pretty seamless once it's put back into place, like you wouldn't notice unless you looked too closely — or if you knew it was supposed to be chipped and you liked it that way.
The cat comes strolling up after the tile has been adjusted and paws the chipped tile until it goes back to what it's supposed to be: a broken piece of tile.
Maybe the cat just likes it that way as a reminder that it needs to be glued and not just pressed back into place. Or, perhaps, the cat thinks the floor has more character with a broken corner. Either way, we suspect that if the tile ever gets properly put back together, this cat will be vexed.