Matrix is doing pretty well (although I might be biased, being project lead). For instance, the entirety of the German military announced moving over to Matrix using a fork of Element a few days ago: https://sifted.eu/articles/european-armies-matrix/, and there are several other (very) major governments beyond France & Germany who are switching to Matrix in order to get end-to-end-encrypted interoperable comms that they can run themselves. Hopefully we should be able to announce them in the coming months :)

Meanwhile, we're about to finish the main milestones of making Gitter natively speak Matrix (planning to announce on Thursday), and on the FOSS side in general, Mozilla has successfully moved over entirely to Matrix for community facing work (https://matrix.org/blog/2020/03/03/moznet-irc-is-dead-long-l...), and a few other similar sized open source projects are in the process of finalising doing the same manoeuvre; watch which this space for updates. https://element.debian.social/ looks to be a thing, for instance :)

In terms of naming, it's really not hard: Matrix is the protocol; the core team set up a company called New Vector who made a flagship Matrix client called Riot, but we then renamed both the company and the app to be Element in order to simplify things. Hopefully most people have forgotten the renaming and moved on by now.

In terms of what's next for Matrix:

* Loads of effort making Element more mainstream-friendly; going through improving the UX and making it consistent cross-platform and predictable for new users. The approach we're taking is to film new users using the service, and literally tight-loop fixing the thinkos that they trip over until they stop tripping over. It sounds obvious, and we should have done it years ago, but it's starting to make a big difference. The first wave of changes ship in the next 2 weeks.

* Social login - implementing OIDC Connect to simplify onboarding if you're willing to hand over your identity to an existing identity provider (Github/Gitlab/Apple/Twitter/Google/FB)

* We're in the middle of implementing Spaces - super fun feature to define arbitrary hierarchies of rooms; a bit like discord servers, or slack workspaces, or possibly a usenet hierarchy or IMAP folder tree depending on how you squint. We're hoping to get the first cut out by the end of the year, which is super fun.

* We're also working hard on freeform threading (you too could implement HN/Reddit/Email/NNTP/Twitter on Matrix if you want!). https://github.com/matrix-org/cerulean has some details for the intrepid.

* Peer-to-Peer Matrix is going great guns; we've just finished the first cut of a new P2P overlay network called Pinecone (based on Yggdrasil, but using source routing).

* We've almost finished a wave of work to make 1:1 VoIP not suck; fixes are already shipping in Element on all platforms, but we're almost at the point where VoIP is robust and reliable rather than a quick proof-of-concept which we'd not had a chance to ever really polish.

* Finally, lots of work queued up to make end-to-end encryption more usable. Particularly, chasing bugs where encryption fails (we just fixed a major one in iOS for instance, which shipped a few days ago, thanks to the Push service extension sometimes racing with the main Element process desyncing). We're also looking at simplifying the E2EE key recovery process and just switching to using the same password to both login and decrypt your messages, rather than separate login password & security passphrases as we have today.

I could go on, but TL;DR: I think "the only one with an open protocol seems to be Matrix, but it hasn't proven to be to their advantage, apparently." is bogus. We'd just be another random open source chat webapp if it wasn't for Matrix; instead it's a global open network with 25+ million users and about 60,000 servers. So not yet as big as Email or the Web, but bigger than (say) bitcoin, and continuing to grow exponentially.