It's 100% open source.
Zulip used to be a company until they got bought by Dropbox (who were after the team, not the product).
Dropbox decided to open source Zulip and tabbott invested and continues to invest lots of (what I assume to be his free) time to make it happen.
The community around Zulip is extremely active and there's lots of high-quality development happening.
https://github.com/zulip/zulip