"Mathematical proofs" are just arguments of a sort. And like any other argument, they can be very rock solid, totally indisputable, or they can be somewhat dubious or weak, even if the the statement to be proven is known to be correct.
The pic in the OP is certainly an argument for the Pythagorean theorem, therefore it counts as a proof.
>>11339249Only applies to right triangles. I can think of a way to sketch up a visual proof for any kind of triangle, but I am lazy.