Does this Fermat's Last Theorem's "Proof" employ circular reasoning? [on hold]

Does this Fermat's Last Theorem's "Proof" employ circular reasoning? [on
hold]

I happened to find this link which contains a "Simple Proof of Fermat's
Last Theorem": http://www.oakton.edu/user/4/pboisver/fermat.html
I don't believe in the "proof" because we can just change III) to be any
statement -- even a contradiction -- and still be able derive it. I'm
still unsure where a problem with it is. It seems that the system is
circular in assuming the truth or falsity of I) in II). Is a problem with
this "proof" about circular logic or something else?
Thanks.