IMHO the article is not mainly about the implementation of the Log, but rather leveraging on the idea of the log to build reliable and fault tolerant applications. The implementation of the log itself can be either centralised or decentralised.

That gist is correct - I would add that the log needs a few specific properties and conceptually be the shared log for state, communication, execution scheduling.

The next step is the, how do you make this usable in practice...