Games certainly are mechanisms, and game-as-artifact tools for fabricating said mechanisms. Recollecting that for TTRPG we can't exclude the players. And the topology I'm describing simply treats those as entries in a multidimensional (and in this case rendered visually) database. The dimensions are the "specific traits, functional and non-functional" and as I said, the sum may be greater than the parts. In saying that the "sum can be greater than the parts" I am saying that as well as traits there are meta-traits.
The topology doesn't "solve a given problem", it's a visualisation of all possible TTRPGs that takes as an underlying assumption that some combinations are more functional than others (and/or they better fit some segment of the tastes of the time). I've described it in simple three-dimensional terms, but obviously it is more than three-dimensional and it would be better to picture modes as dense or hot spots in the volume.
By "specific" you could mean that the "traits, functional and non-functional" of the mechanisms are such that TTRPGs are incommensurable. Seeing as that would contradict or void the comparisons between modes of play that many in this thread are making, I'm assuming that's not what you intend, right? It'd be a pretty radical claim so let me know: it'd be interesting to entertain it. For one thing, it'd mean that comparisons folk are making between modes are meaningless.
Were it true, then yes, games would each have distinctly different lists of dimensions and couldn't be mapped into the same conceptual space. They would still be mappable on the basis of any dimensions they shared, which is what I've observed in this thread, unless folk are making much stronger arguments for privacy or exclusivity of the "traits, functionl and non-functional" than I am reading them to.