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)