Its a really really tiny star; quite small even as M-dwarfs go. So its habitable zone cannot but be where it could tidally lock the planet. Now, maybe some other resonances are possible, perhaps if there are other bigger planets around it helps (and I think they didn't exclude something up to a size of Neptune at about 1AU or beyond); don't know how the orbital mechanics of all this work out.
But there were various modelling attempts to see how a tidal lock affects the climate, and it may not be a dealbreaker; not too thick an atmosphere could effectively transport that heat around, at least so that it doesn't risk freezing the atmosphere on the dark side and making it uninhabitable. But its just modelling so..
Maybe even more problematic is that a tidal lock could imply no internal dynamo, and so no protective magnetic field, and Proxima flares quite a lot, so it could have totally eroded its atmosphere and sterilized the surface with UV etc. Plus Proxima was much much hotter early on; would that period have permanently made the planet uninhabitable?
We just know so very little about habitability of M-dwarfs, and particullary the really small ones; we'll just have to find out,
Before we took a close look with probes, we thought Mars had lichens living on it, to explain its color variations or some such; there's no reason to think we have any more clue about M-dwarf planets than we had about mars then, for we have yet so study any.
Good thing one just happens to be in our backyard :D Though realistically, perhaps it turns out easier to study more distant M-dwarf planets, because this one seems not to transit from our perspective. And I think we could study the spectra and hence atmospheric composition of transiting planets sooner than we can hope for direct imaging of them. Not perfectly sure though.