The domain of astronomy is the starry sky and the Universe it reveals. The domain of surgery is anatomy, physiology, metabolism. In Informatics (not everyone calls it "Computer science", eh?) the domain is formal systems.
In each case the instruments (telescope, scalpel, digital computer) are not the main focus of investigation, they are tools, not the domain of study.
> the computer is the central figure
This is precisely the misunderstanding that Dijkstra tilted against.
> can you think of ANY other tool that represents CS?
Yes. The human brain.
I'll leave you with another joke, one of my favorite, although I don't know who said it, "Computer science could be called the post-Turing decline in the study of formal systems."