This looks like an interesting, but a bit strange, old story. A bit similar to parts of an earlier posted essay by Gromov. However that may be, the Princeton IAS invited the author and so I'd like to know about how his concepts are intended to become implemented and applied:

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I did not open the paper. Take a look here regardless though and see if it is what you are looking for.

Not quite so. The n-Lab contains a page on it: , but that is not that new. The usual deficiency of such constructs (and the many attempted definitions of n-categories) is their reliance on set theory. Grothendieck seems to have been the first to suggest to forget set theory as foundations, and Voevodsky's way to build a homotopy-theoretic foundation of mathematics on some sort of computer language (leading to entirely new approaches to artificial theorem proving/checking): may be interesting for Baas' ideas too. Interestingly too, homotopy theory, n-category were caused by attempts to deal with topology, and Baas' concepts come from the same background. He was apparently motivated by Charles Ehresmann's ctitique that n-categories should be insufficient.