I think Rocket Chat started development after the Slack craze and tried to fill the niche of being an open source version of the latter. Since I last used it, it seems like a good alternative for on-premise, open source Slack-like, still.

Now that we have Matrix, I'm not sure where it's place is but I'm sure some orgs are fine using it for internal communications without having to pay Slack for your history/premium features?

It has administration features accessible in the UI that no Matrix client does. The capability to edit other people's posts as an administrator without having to go into the database is very useful for when somebody can't update something important, like an announcement. Generally, it's far more customizable out of the box, without having to rewrite parts of it, and many features taken for granted in it are not supported by any Matrix client so far.

The downside is that it is, and always has been, incredibly buggy and prone to total failures.

A few years ago when we needed an on-prem chat tool (around the time Atlassian killed HipChat), rocket.chat had the benefit of being easy to set up. For Matrix you needed a Synapse (Dendrite wasn't ready back then) backend, a Vector frontend, some arcane backend for authentication, and you had to connect everything together by hand, while rocket.chat had a docker-compose file you could add Keycloak to and spin everything up with a single command.

I think it was around first -- my university CS department used to have one (cheers to whomever at WSUV made that a thing).

It's made more for company/enterprise use, instead of public communities like Matrix is geared towards.