Hi Josiah,
I get the feeling there's mostly a philosophical point you'e trying to make but reading the wikipedia article on Quine I would say TiddlyWiki sure ain't one.
I'm also not sure why you think the notion would be particularly useful for TiddlyWiki beginners. In what sense?
Yes, TiddlyWiki does not (try to) produce a linear output or experience. However, "procedural" does not mean that. The state of a system depends on it's input-output relations, so even a "procedural" bit of code may behave in nonlinear ways, hence all the more reason to consider approaching things models more from an object oriented angle, rather than a mere procedural unfolding of commands against plain digits.
You said: //Its open-endedness is a signal marker of "Quineness".//
Where does it say that open-endedness makes for a quine? As far as I can see it's sole purpose is to, well, render it's very own source and that's it.
In general, I think the era when we thought of software as purely strict, logical, "deterministic" is long gone. Perhaps people would imagine assembler language to represent that kind of thinking, tic toc makes the clock, but even there you can get to some quite non-deterministic states at the intersection of hard- and software.