Definitely going to look into this when I have the time. If it's not using your Apple ID for authentication (like the article says), what's to stop anyone from spoofing anyone else's phone number?
The pypush readme doesn't have a lot of details so I guess I'll just need to try it to see.
Edit: Looks like he's distributing "a framework from an old version of macOS, in order to call some obfuscated functions", which the script pulls from his GitHub. This is likely a copyright violation. If Beeper Mini is doing the same thing, I'd expect them to get sued into oblivion the second Apple takes notice.
It's not clear which version of macOS he pulled this from. There's always the risk that Apple will simply axe support for it. I don't recall them breaking support for older OSes with iMessage in the past but I haven't followed that closely so I'm not sure.
Update:
Just ran it on my desktop. It immediately prompts for a username and password, presumably for an Apple ID. I didn't continue because I don't want to use my real Apple ID. The article says Beeper Mini doesn't need an Apple ID at any point. After a little searching, it looks like iPhones actually don't need an Apple ID to use iMessage. I was not aware of that. So I guess Beeper is not using the exact same mechanism as pypush.
Beeper has been working in this space for awhile - there's no way they would publish an app with a copyright violation. I assume they have a workaround for that aspect.