I think we do gain a little bit by saying "classical" instead of "digital".
As you point out, you can certainly build classical analog computers, and in the past these were very useful. But I believe that such classical analog computer can all be efficiently simulated by digital computers - not in the sense that a digital circuit can necessarily mimic the exact physical evolution of the computer, but in the sense that they can in principle solve any given problem with a similar asymptotic runtime (possibly up to polynomial speedups or slowdowns). In other words, I think it's generally believed that the extended Church-Turing thesis holds for all physically realizable computers whose behavior does not essentially rely on quantum mechanics. (You might argue that this claim is vague or even circular, but I think that with some work you can make it both true and noncircular. Note that this claim certainly hasn't been rigorously proven, but I think it's generally accepted to be true in our world.)
So I think that referring to these computers by the broad term "classical" usefully conveys the highly nontrivial insight of the extended Church-Turing thesis: that if you just care about "macro" features like the asymptotic runtime, then it doesn't actually matter whether your computer is digital or analog - what matters is whether it can use inherently quantum phenomena like superpositions and entanglement in a controlled fashion.
Edited to add. James Wootton asks in a comment whether it's been proven that classical analog computers can be efficiently simulated. The answer is no, but I personally think that that question is making a bit of a category error. The way I see it, the extended Church-Turing thesis is not quite a sharp enough statement to be mathematically provable or falsifiable (although restricted versions may be). It's more like a general principle that evidence can accumulate to either suggest is useful or not useful. (More along the lines of a statement like "All physical regimes can be described by some type of action principle" than a mathematical proposition.)
By the way, I highly recommend Scott Aaronson's paper "NP-complete problems and physical reality" (PDF), which proposes a claim somewhat similar to the extended Church-Turing thesis - that no physically realizable process at all (classical, quantum, or whatever) can act as a computer that efficiently solves NP-complete problems.