The problem with all these arguments is that DOS extenders of the day used to do the same, or more. Do you call DOS extenders "operating systems not shells" too ?

On one hand you have that the technical answer to the above question is likely "yes". DOS is so simple that any non-trivial application likely qualifies as an operating system. Implementing some kind of virtual memory support is almost a given, and process control is not unheard of.

But on the other hand most people would refer to anything pre-95 as "shell" for the simple reason that it requires DOS to boot ; even when complexity-wise, 95 and later versions of 3.x are practically the same: if you call one an OS, you ought to call the other one a full OS too.

So this question is on the "angels on the head of a pin"-level; but this simply means there's no answer that doesn't require a lot of nuance, and this also applies to the "it can't be a shell, it does too many things" answer.