Nope. That still supports backreferences, and resolving backreferences is an NP-complete problem.[1] And I don't see anything in that paper that addresses that. Note that there may be some versions of the problem that maybe aren't NP-complete[2], but again, not addressed by that paper.

Besides, that paper was published 12 years ago. Where is the productionized version of it? Or are you suggesting the the OP go spend a few years writing a regex eninge? :-) Doesn't seem like a particularly practical suggestion.

[1] - https://perl.plover.com/NPC/NPC-3SAT.html

[2] - https://branchfree.org/2019/04/04/question-is-matching-fixed...