Why not WhatsApp? Isn't it peer reviewed by Signal?
I know the OP didn't mention about a platform being dependent on having a mobile phone number...but an advantage of matrix is that it does not require such a number. I state this because the OP focused on desktop, so i am making an assumption here. Also, matrix (and other federated-based platforms) need not be hosted in a single silo...much like email, can be hosted by numerous servers, and yet interact freely.
I've never heard of it being peer reviewed by Signal.
And even if it is, there's a lot of stuff around Whatsapp apart from the protocol that most likely is not.
It was Open Whisper Systems. My bad.
They're the people behind Signal, kind of assumed you meant them :-)
The desktop client is still a resource hog though, I hope they'll manage to improve it. Matrix is the main reason I still use IRC channels (through bridges).
The riot.im website isn't bad from resource usage perspective. At least doesn't bog down my machine...though I'll admit "a website" may not fulfill OP's request for desktop app.
There are various desktop and mobile clients. Matrix is just a protocol.
The website is ok indeed, I should have mentioned that I was referring to this client: https://riot.im/desktop.html.