And it is certainly not surprising that amateurs in general forget that F = ma is only valid if the mass does not change. The more general expression is F = dp/dt, where p is the momentum. But this, of course, is also only valid in inertial systems. It's not really important to the article but it does kind of annoy me that he uses the most special case of an expression in an argument about it being general.
He could have actually made the point about generality by comparing this expression to the most general one for the force (in a frame of reference that accelerates). That would have also shown why generality can quickly become infeasible in practice. If he knew how many approximations people make in the real world, not because they want to, but because they HAVE TO, his worldview might be a different one.
I feel like he's trying to make a point about a very specific scenario but doesn't mention it explicitly. Instead he tries to be general and therefore fails to understand that his view doesn't actually apply in general.