"centralised" and "server" are just about the worst words you want to hear in the description of a system like this and yet they are just thrown in there in a flippant comment at the end of a section?
I think a more detailed description of this glorified cache is warranted.
To cut a long story short: Alice gives the cache, aka Mallory, a set of secret data which are implied but not proven to be able to be used by Bob to create cryptographic text which Alice can decrypt but this magic cache, aka Mallory, cannot. This document provides few hints and no detail on how we can be assured that the magic cache, A.K.A. MALLORY, is unable to make use of the secret data provided by Alice (and "promised not to be shared") to make inferrences on the crypyographic text provided by Bob.
So: making the whole thing completely public only enables adversary to match session initializations with receivers, which the server can do by definition as it has to route the messages to correct recipient. (In the case without such central server, anybody observing the traffic could do that, as another role of the central server is to mask sender addresses on the lower protocol layers)
I know that doesn't sound quite so impressive, but that's because it isn't.
Additional and to some extent non-trivial difference from traditional OTR is in how these ephemeral keys are used in key exchange, whose result depends not only on DH with ephemeral keys but also on DH exchange that mixes ephemeral keys with long term ones. This causes that the ephemeral key of the passive side does not have to be signed and allows anyone to produce arbitrary session transcripts, both of these points allow significant reduction of size of the exchanged messages.
Or would have been, if they had any.