How does this paper support your claim?
They argue that "the generic formulation of string theory leads naturally to dark energy", then propose the supporting mathematical equations to support some models. They do not claim in any way that "dark matter is the root of string theory".
Whether non-baryonic matter can be detected by any other means than gravity is unknown. I'm not sure how one could claim for sure that it is impossible. That does not appear to be discussed in the link provided though, and there is sure is still hope that it can be, even if the detection of axioms have so far been deemed false positives.
In this specific case, the supporting data you claim missing is from Hubble, and stated so in the paper:
https://ancillary-proxy.atarimworker.io?url=https%3A%2F%2Fiopscience.iop.org%2Fart...
The math can be proven wrong, the model(s) demonstrated erroneous or the argument counter argued, but it seems that has yet to be done.
It is perhaps it is a matter of perspective, but whatever the facts will prove themselves to be, they would to some appear "extraordinary" anyway.
Although it did not serve its intended purpose, thank you for the link.