Indeed, it sounds like the author is looking for the UNIX of the 21st century:
* Widely reusable meaning: everything behaves like a file. The types of files we can have are defined by specs: an Image can be described as a PNG file, which every process can understand. A table can be a CSV or a SQLite file. A Conversation can be a maildir folder. We might not have the best descriptions of "things" but we do have something
* Data without borders: if you can read from stdin and write on stdout, you can interact with the data. In fact, joining two tables is a base task and can be done with join (https://linux.die.net/man/1/join)
* Inherent, ubiquitous programmability: I'm not sure I understand the author's point, but it sounds like the entities in a software are too specific to the program. Again, if every "application", or rather set of utilities, used the filesystem with clearly defined specifications for what data is, then they can work together
What is not following the UNIX guidelines is definitely the Web and mobile platforms, as the author focuses on. There were some attempts at doing things the UNIX way, like uzbl (https://www.uzbl.org/) where every thing is a script away, or ii (https://tools.suckless.org/ii/) which gives a filesystem interface to IRC conversations. Want to parse a message ? It's just a string in the filesystem, any script can do it.
There's a reason it didn't work as well as we want, and it's that in practice it's all clunky and hard to maintain when the alternative is a single, unified application. Especially when the alternative is from a commercial vendor with a lot of cash. The incentives of doing FOSS that interacts with each other are not aligned with making money.