The device in question is, at best, a calculator. A slide rule computes in the sense of a calculator; but, it does not run a program. The Antikythera mechanism is like a multi-tiered circular slide rule.
I don’t suppse you’ve ever heard of a mechanical computer.
Are you being serious?
The evidence for this device being an astronomical computational instrument places computational code within its mechanical components.
If we were provided the engineering specs, a number of us could write the program embedded in those gears.
“Computer” is semantics. In the era in which it is believed to have been assembled, it is the equivalent of a Cray 1 existing in 1940, before Colossus came about.
It is truly a computer, the irony being that even today it is beyond most people’s comprehension.