The author is simply sharing their preferred messaging apps, and they describe the criteria used. Sure it's not an objective in-depth security analysis or a result of professional audits but it's also not claiming to be those things, right?
Understanding the threat model isn't an "in-depth security analysis", though. It's just a matter of understanding why you care about secure apps - who you want to be secure from. If you don't know that, then these are just toys, and you're just playing.
Great! Some of us like play.
The introduction implies some level of security analysis based on the list of "criteria" (e.g., "does not expose personal information" and "does not leak data") and the "testing setup" link.
Does not expose to whom? Leak to whom?
That's exactly my point. Ask the author. They implied that they did some analysis beyond trusting claims made my developers, but there aren't sufficient details.