These statements are mutually exclusive: End to end encrypted: Nobody, not even us, can read or listen into your conversations. Works everywhere: Visit subrosa.io from any computer. No download or install needed.
If you don't run your own server, the site's claim that "nobody, not even us, can read or listen into your conversations" doesn't apply to you.
There's nobody to whom both claims apply at the same time!
The developers might well be thinking along the lines that you describe, but I don't think that a visitor to the site is likely to understand the threats that way.
Edit: Looking at https://subrosa.io/security I think it's even more clear that they're making these claims for their own hosted instance of their software -- and that's what people here are most skeptical of.
Subrosa's value proposition is more as a meeting place then as a "secure" chat software.