I think part of the problem is that mathematicians are just surprised something like this was published in the NYJM in the first place. It's like publishing a sci-fi short story in a literary poetry journal -- a genre mismatch to begin with. It's not usual in math for a journal like NYJM to publish a "we propose a model for a bio problem & look it gives this kind of result". That's not a math paper. There's no theorem. How does it advance our understanding of the underlying structures of mathematics?
Papers like that are far more often published in applied math (look, we can apply this math to that problem) or computer science (look, we can apply this ML algorithm fruitfully to this type of data, for instance). I have sympathy in trying to find journal homes for these types of papers, because I'm looking for journal homes right now for some very interdisciplinary papers (applications of topology or algebraic geometry to finance). Often it seems you have to have really amazing results so you can publish in a general-interest science journal, because the math journals are so specialized they won't consider something like my papers or this paper.
You don't have to accept anyone else's judgement on the quality of the paper, although Tim Gowers is a guy who knows his math. A cheap shot here is to search for the word "theorem" in the provided arXiv text. Doesn't appear. Ok, the authors are so modest that they only prove propositions, not theorems -- but that is a sign it's not a real math paper! Then look at the propositions themselves. Prop 7.1, the first of a grand total of three propositions in the paper (no lemmas): a particular normal distribution is more variable than another if the... variance of the first is bigger. Wow. Sure, the authors say "the following simple proposition may be well known" but dang, this is not groundbreaking. This is barely mathematics.
Try following through the proofs of the three propositions. It really is at an undergrad level -- I'd be happy assigning some of these 'propositions' as homework exercises in the class I'm teaching now except we have more useful material to cover. There are also some problems the authors should have addressed regarding the subpopulation assumptions, etc. A good article of this type would have done additional modeling to address that. If I were reviewing it, I'd like to see a breakdown say of the different results given initial values of parameters (I'm a total sucker for wall-crossing or regime-change-type results -- like, cross this wall in the space of parameters and the behavior of the model will change in this way. Think phase planes in differential equations: https://en.wikipedia.org/wiki/Phase_plane or regime-change results in economics). A dynamical systems analysis would be cool, but I'm biased like that. Analysis of robustness or sensitivity would be nice. I'd want to see comparison with other models, or applications of these models to other topics. The author could have replaced the non-math appendix full of useless crap with this material.
It's really important to be able to argue that your model isn't just a one-trick pony if you want to call it math -- you need to show it's a useful model with interesting mathematical properties that you can elucidate in the paper. This paper doesn't do that.