I don't speak for computer scientists but I have advanced training in statistics and I think of Computer Science / Statistics as mathematical sciences: they're born of mathematics and have become distinct because of practical considerations.
Both terms are fluid. Most theoretical computer science research is essentially mathematics, at a high enough level. Some wouldn't necessarily call themselves mathematicians unless their graduate training was in a math department; some might. Some would call themselves scientists insofar as they consider mathematicians a subset of scientists. Most would not consider themselves scientists in the sense of natural sciences like biology.
But, most probably don't have a strong opinion on whether/which labels apply! They would say they just do research in TCS.
He has said something to more or less the same effect:
it was firmly implanted in people’s minds that computing science is about machines and their peripheral equipment. Quod non [Latin: "Which is not true"]. We now know that electronic technology has no more to contribute to computing than the physical equipment. We now know that programmable computer is no more and no less than an extremely handy device for realizing any conceivable mechanism without changing a single wire, and that the core challenge for computing science is hence a conceptual one, viz., what (abstract) mechanisms we can conceive without getting lost in the complexities of our own making.