My lowest level definition of a computer is any machine that is “Turing Complete.”
If it was built (which it wasn’t), Babbage’s “Analytical Engine” would have been Turing Complete. This was the 1830s.
This is important as it is a precise definition that we can start with, then argue about further additions. E.g. Is a stored program required? Does that game have to be able to run in a reasonable amount of time (i.e. is it playable)?
Some calculators would be Turing Complete I reckon. We’d have to look into it.
The earliest Turing Complete computer is something like Konrad Zuse’s Z3 (1941), but as it lacked a condition branch instruction, it was (is) only theoretically Turing Complete. It’s this sort of boundary that is interesting. The answer lies, I’m pretty sure, somewhere between 1941 and 1951.