From the abstract:

This approach to language (which they call ‘Dynamic Syntax’) is fundamentally different from orthodox generative grammar and conceptualises syntax as procedures for interaction.

I'm not a specialist in RT, so I can't comment further from that perspective, but if you're asking whether this is a mainstream idea for approaching syntax, no. That doesn't mean it's not a valuable idea, but it's just not widely used, primarily because it seems like it's from the perspective of Pragmatics, rather than something that syntacticians work with.

You would need to (and maybe should) ask an RT specialist for a more specific perspective on this.

Regardless, I wouldn't discourage you from looking at less mainstream ideas if they seem relevant and useful for you. If you want to focus on the main ideas so you can follow the literature in general, this probably isn't it, but if you're interested in exploring ideas yourself, there's nothing wrong with less popular ideas, especially if you work out how to connect them to the more popular ideas: for example, why is this approach different/needed/better than others? why propose it at all? If you can understand that, then you're doing well. Sometimes it's less about the "right" theory and more about asking useful questions.

(From the perspective of Syntax, this sounds vaguely more like Construction Grammar than Generative Grammar, so a starting point would be figuring out how exactly this approach differs from Construction Grammar, and whether it's reinventing that wheel, or (in)compatible with it, etc. There's also this: https://en.wikipedia.org/wiki/Systemic_functional_linguistics)

My primary interest is in pragmatics, so this as an interface between pragmatics and semantics is something that interests me. ... I don't think that it is reinventing the wheel...

The (potential) problem is one of perspective. There's no need for a unique "pragmatic" approach to syntax. There may indeed be a need for syntactic theories to take pragmatics into account. But driven from the perspective of pragmatics, this likely either won't catch on and might just reinvent that wheel in a limited niche. Linguists theorize a lot, but often don't reach a consensus especially based on ideas from outside of a specialization. And often ideas like this bring up legitimate problems but stop short of actually solving them (especially in terms of communicating the problems to specialists in the subfield). The real trick is to actually integrate different approaches effectively: have syntacticians and pragmaticists benefit from collaborative research. It happens. But it should happen more (across all domains: all of the above can be said about syntactic ideas about pragmatics too, and other fields).

This is just some thoughts about how to navigate the literature, not an evaluation of the ideas themselves. The result is, as I said, that non-mainstream ideas are sometimes important. But it does make navigating the literature difficult!

I found this site, that seems a touch like the Relevance Theory Online Bibliography that Dr Yus maintains but for Dynamic Syntax


http://www.dynamicsyntax.org/publications

They give a link to one of the books that is free on ResearchGate
https://www.researchgate.net/publication/298544659_Dynamics_of_Language_An_Introduction

Sorry, another question.
Page 34-35, I am getting confused re. the numbering here

In figure 10, is the number 0 next to the first up arrow indicative of the current node being an argument node, rather than describing anything about the mother node that it relates to? If so, this seems to be the reverse from figure 2.11 where the number annotating the down arrows seems to relate to the position of the daughter node as an argument (left) or functor (right) node

Also, according to 2.11d =, it looks like this is being read bottom up - this seems to be different from 2.10b?