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This is indeed a very elegant fastening method.

I wouldn't be surprised if the designer of that CNC machine borrowed it from the popular Prusa MK2 3D printer, which uses a very similar design for its Y-axis belt: https://help.prusa3d.com/guide/2-y-axis-assembly_79992#81120

It's been a standard method for decades. Theres a lot of cases where even the center post isn't required as the zero radius 180 won't fit back through the slot.
That center pin looks fragile, especially if it's printed along Z axis. How about printing teeth that'd mesh with the belt?
If you printed teeth, you'd have to make sure the teeth in the top loop are precisely aligned in relation to the teeth in the bottom loop based on the length of the belt, right? That seems like it could be limiting
A small bolt could easily replace the pin, this would also allow a washer to be added preventing any chance that it working loose.
Author appears to have concerns about the belts working out of the top of the housing, but is seemingly ignoring the four existing screws that could be used to fasten a top plate to prevent this?
or, if you upped the pin diameter, you could thread a hole through the pin and throw a washer on top
This is why I thoroughly enjoyed building my Prusa as a kit. You see little tricks like this, including this exact one. Or how they embed threaded nuts, or how the print is shaped and oriented to be made without supports, etc. Building the prusa saved a bit of money, but was also a crash course in how to design.
Making your own tools is a time-honored tradition, partly for this reason.
Also works well with a zip tie or 2. The belt holds itself in place as long as the tension is there.

Most of my old printers still use this method on them. [1] You can also use another ziptie as a tensioner.

[1] Very old example. https://flic.kr/p/db51Ue

FTFA

> Attaching the timing belt while maintaining tension can be somewhat challenging

Sounds like a bad design: no tensioner? How do you take up the slack as the belt ages?