I have a hard time understanding the author's point of not using UML but somehow boasting that they used "plain old boxes and arrows" to create "plenty of diagrams".
UML is nothing more than a bunch of "plain old boxes and diagrams", but which have concrete, objective meaning that has been specified and thus help share ideas as objectively as possible. UML is a language, and languages are tools to communicate and share information.
Using ad hoc box and arrow diagrams invented as they go along means they decided to invent their own language, which may or may not be half-baked, that is not shared by anyone other than the people directly involved in the ad hoc diagram creation process.
If the goal is to use diagrams to share information and help think things through, that sounds like a colossal shot in the foot. I mean, with UML there are documents describing the meaning of each box and each arrow, which help any third party to clear up any misconception. What about their pet ad hoc language?
In the end the whole thing looks like a massive naive approach to software architecture, where all wheels have been thoroughly reinvented.