A walk down memory lane on one of his previous attempts to demonstrate he was Satoshi:
The one positive thing I can say about Bitcoin is that it gives someone who is factually Satoshi an extremely easy way to prove that fact in a way which is extremely difficult for anyone else in the world to forge. Wright hasn’t because he can’t because he isn’t.
This is the problem that Keybase is trying to solve, though I don't have enough experience with their system to know how well they succeeded.
What is that way?
I read your link but my layman's brain couldn't parse it... well enough to understand it.
Write a message like “I am Satoshi. Here’s a boring detail which proves this message was created on demand.”, sign with corresponding private key, post the ~10 lines of OpenSSL commands which verify that the signature matches. The end.
Details of public/private keys, hashes, etc are important, but at the core the idea is simple.