This seems like a theoretical modelling paper (all of its figures are simulations?) that contains as far as I can read 3 (!) actual experimental measurements in bulk on a fluorospectrophotometer. The claim is that the increased fluorescent quantum yield (QY) of microtubules over tubulin can be explained by the ideas in their simulations.
It's hard to buy that their proposed stories are the simplest explanation for these few measurements. Much more boring phenomena can influence QY. e.g. simply occluding fluorophores from the bulk solvent can have a huge influence on QY.
The TL;DR is that this paper claims to have found evidence for quantum effects in microtubules, lending credence to (though by no means providing proof of) Roger Penrose's theory that consciousness is a quantum phenomenon.
I don't think the study authors would endorse the claim that this meaningfully lends credence to Penrose's theories about consciousness. Quantum effects are all over chemistry; that's nowhere near sufficient to provide much evidence of quantum computation happening, which in turn would not necessarily suggest any kind of explanation of consciousness.
Nobody is skeptical about quantum effects (of this sort) happening in biochemistry. All of the skepticism Penrose faces is about the quantum computation and consciousness parts. So this paper won't change anyone's minds about Penrose.
It's hard to buy that their proposed stories are the simplest explanation for these few measurements. Much more boring phenomena can influence QY. e.g. simply occluding fluorophores from the bulk solvent can have a huge influence on QY.