Note that the regression is on the differences, y_t - y_t-1 not the levels, just y_t.
So the argument is more subtle, that the "change" in AirBnB share is correlated with changes in rents. So level effects such as being a nice neighborhood are accounted for.
Having said that, a large change in AirBnB share is probably still related to unobservables related to factors that would increase rent. E.g changes in hipness of a neighborhood unaccounted for by changes in demographics. Therefore the $616M figure is biased upwards, though I bet in reality still a large number.
So the argument is more subtle, that the "change" in AirBnB share is correlated with changes in rents. So level effects such as being a nice neighborhood are accounted for.
Having said that, a large change in AirBnB share is probably still related to unobservables related to factors that would increase rent. E.g changes in hipness of a neighborhood unaccounted for by changes in demographics. Therefore the $616M figure is biased upwards, though I bet in reality still a large number.