Not much. I think he is crying conspiracy theory or it is a satirical take of drcraigwright.net/jean-paul-sartre-signing-significance/
I haven't ruled him out of being SN in my mind yet but he has to do one of two things (or both) if he is going to prove it to the world:
1) Sign a message saying "I, Craig White, am Satoshi Nakamoto" using one of SN's private keys.
2) Perform a transaction using a coin from Block 9 which is the only mined block to be known 100% to have been mined by Satoshi Nakamoto. Block 0 was Satoshi's but you cannot spend coins from the genesis block.
Either of the above would be enough to prove that he is Satoshi Nakamoto or or has acquired access to his encryption keys.