Not a valid mathematical argument. However, this is more of a philosophical line of reasoning. The fellow you link to appears to be arguing that space is discrete, not continuous. I happen to think that the discreteness of space is a fantastic answer to Zeno's paradox (motion is then possible by quantum mechanical tunneling). I don't buy the standard calculus answer. However, that is neither here nor there.
If you assume space is discrete, then the axioms of the real numbers go out the window. If that's the case, it might be that the proof of the transcendence of is severely compromised. That would be the place to look: the proofs of the transcendence or irrationality of . If all those proofs depend on the axioms of the real numbers, then this guy might be on a somewhat firm footing. If, however, there's a proof that does not depend on the axioms of the real numbers, then what he says is suspect.
That's my two bits. I could be entirely wrong!