Looks like they forked _a_ Matrix messenger (FluffyChat, which I haven't heard of before and which doesn't seem to be "the" official Matrix messenger, if such a thing exists) and are running a non-federated Synapse server on the school premises.

That sounds like an overall good idea to me. The client fork might be questionable, but it's clearly targeting a non-technical audience (or, not necessarily technical), so having a low barrier of entry makes sense to me. Kudos to them, hope they can keep it maintained.