The argument opposing the minimum wage is not that it hurts businesses equally, but that it focuses the pain on businesses and workers at the margins. Here we have a business that for all the reasons you point out is a marginal business, and this price shock pushed it over the edge.
It should be somewhat tautologically obvious that the businesses who have the hardest time absorbing a price shock like the minimum wage are the ones that are struggling already. This can be ignored with regard to large-scale industrial policy only if you feel there is no value in marginal industries. But keep in mind that almost all businesses go through "marginal" periods eventually, either on the way up or the way down (or both, sometimes multiple times).