It's got a lot going for it, I think... cautiously. By not modelling theoretical variables, and simply looking at what has happened in the past, he negates a lot of the usual uncertainties. It doesn't matter that he's not covering all the variables, because there are always lots of variables, and when the data are this messy, then broadly they should cancel out. Unless the current global situation is fundamentally different to the past, of course, in a way that it never has been before.
Given that messiness, though, what you can't do is predict exactly when the threshold will be crossed... because clearly there is variability in the threshold depending on the specific parameters (tectonic, biological, geochemical) of the time, as well as what we do on route. The paper's pretty clear on that as well. I note that we're in range of some of the scenarios already (given his presumed 50% error margins).
I'm not entirely sure that this is telling us much that is new, though, beyond the details. We know that there are points beyond which acidification and temperature rise are very bad news, and 2100 is a time by which pigeons will be well and truly home to roost. What this does, though, is give us more confirmation that the models and urgency are reasonable in predicting the worst scenarios. Not only do the theoretical predictions point to all this; the past does, too.
Note, however, that I've not gone through his methodology in detail - there might be some glitches lurking there that could knock it down. I suspect not, though; take a blunt-instrument approach, and it's hard to find a way to push it over completely.
Thanks for bringing it to our attention!