Found this quote that sums it up nicely.
Digital general purpose computers are programmable by the means of a set of discrete operations. However, this doesn't generalize to include all sorts of computers.
* edit just to add your quote is definitely wrong. A CPU is a set of logic gates that executes a fixed set of operations.
People have used the word “computer” for a lot of non-programmable machines over the years, and it’s clear in the Wikipedia article I linked to that programmability is a recent feature of computers, and was not always there. (Nor is it always there to this day.)
While I’m sure you can find examples of people that agree with you, that doesn’t invalidate history. A computer is anything that computes something, that’s how the word has been defined and used up to and including today. This includes the Antikythera (analog computer) and even (loosely) the Abacus (digital “computer”).
We're in a very weird transitional phase for a lot of this kind of thing. It's still largely a fixed set of operations, but it can be re-programmed and in theory isn't completely restricted to just those functions. Someone could port doom to it (I do actually want to see that one).
In the 1940s, there were computers, such as ENIAC, that were programmed with plugboards that changed the connections between modules that performed various mathematical operations.
If the modules in the Nimatron could be reconfigured to perform other operations, the Nimatron would, by the standards of the era, be considered an electronic computer, even if today we usually reserve that term for Von Neumann style machines where the program consists of symbols stored directly in the machine's memory.
The Online Etymology Dictionary states that the use of the term to mean "'calculating machine' (of any type) is from 1897.
The Online Etymology Dictionary indicates that the "modern use" of the term, to mean 'programmable digital electronic computer' dates from "1945 under this name
So computer is the correct term before 1945.
https://en.wiktionary.org/wiki/compute
I'd be inclined, though, to exclude "non machine" counting tools such as an abacus.
It might be easier to think of mechanical computers, such as the WW2 fire control computers aboard Navy Ships[0] or more famously the Antikythera mechanism[1]. These are fixed devices, they compute values from inputs. The "program" is stored in the gears camshafts and differentials and ratios between them.
Similarly, fixed digital computers such as the Nimatron have their operations stored in relays and digital logic. These sorts of computers don't have a list of instructions. They just have schematics, inputs going through electronic circuits that wind up at outputs. You can do a lot of calculating with just simple logic gates.
How can a computer be non-programmable? The whole idea of a computer is that it runs a list of instructions.