Couldn't they just use a Merkle tree, like git does, to keep track of the history? I think that's what he's referring to here. They don't need proof of work if the code that can modify the history is trusted.
Merkle trees don’t solve the forgeability issue, just the unbroken chain of what you currently have. So, if you have control over the server you can just create a set of events with your “+5 billion gold” event injected in it, recalculate the tree and root and voila: forgery.
PoW doesn’t prevent this, it just adds computational time provably spent between the events so that if you DID try to inject a false record a year ago you’d have to spend that same amount of time calculating the resulting merkle tree.
Merkle trees all the way down!