2 HS students from NOLA shake up the world of math in a huge way...

No, thats not what they did.

Many non-trigonmetric proofs of Pythagorean theorem exist.

What they are trying to show is a trigonometric proof of the Pythagorean theorem, that does not involve circular reasoning i.e., contain the Pythagorean theorem as one of its implicit assumptions.

You're really struggling with that analogy. Read it again, that's exactly what I said. Of course it's not what they did or what they were setting out to do. You criticized them for doing a proof using trig by comparing it to the people who proved the theorem without using trig.

Based on your earlier post, it seems you're just catching on to that fact and trying to change your tune. At any rate, I have no faith you will correctly interpret their proof.