Good question! Had to look it up in the paper, and it turns out they use wood screws.
Either regular ones using a long screwdriver through one of the bottle's mouths, or more specialized double-ended screws (with two points) that let you grab the bottles and counter-rotate them to drive in the screw in both bottoms.
Neat, I hadn't thought the bottoms of PET bottles had enough material to make this work, I would have expected bolts with nuts, i.e. more metal-to-metal in the fasteners.
I have an idea that I haven't tried yet. 3D print hollow joints that, for example, connect wood panels into a book case. Then fill the hollow spaces in the 3D printed joints with concrete.
That has potential, though it may be hard to find a shape that's open enough to get concrete packed into, while still wrapping around the panels effectively (and you'd want to use a concrete with fibers mixed in to help with shear[1]). It might be possible to use epoxy resin instead.