AIUI, the Z3 has no conditional branches. Without those, it's not much like a computer as we understand it. Rather, i think the Z3 is an "automatic calculator" - it can carry out a fixed sequence of operations, but it can't do arbitrary computation. In that respect, it is like the Atanasoff–Berry computer and the Harvard Mark I.
The prehistory of computing has a bunch of really interesting machines like this (and Colossus, and early ENIAC really) which are technical marvels, but miss at least one of the key things which make a computer really a computer.
People often focus on the electrical vs mechanical distinction, but that's a red herring. If you made a 386 out of Lego, it would still be a computer. Similarly, binary vs decimal is irrelevant.
To me, there are three key characteristics:
1. There is a program comprising a sequence of symbols which are interpreted by the machine (so not Colossus or early ENIAC, which were controlled by plugboards)
2. There are symbols for conditional branches, or some equivalent construct, and the language is Turing-complete, or some practical projection of it (so not the Z3, ABC, or ASCC)
3. The program is stored in a memory which can be modified by the program
Once you have those things, you can do anything. The first two points are the most important, but i think the third is also really significant: it is what allows things like operating systems and linkers to arise. If the first two are the definition of life, the third is the definition of multicellular life.