I think the distinction is that Antikythera was a calendrical device, but couldn't perform multiplication/division etc of a given number like the device described here.
If anybody is interested in the construction of this device, definitely check out ClickSpring on YouTube. He's doing a full build and also exploring techniques and materials that might have been used way back when.
Do you mean that you saw the ClickSpring reconstruction in person, or the Antikythera mechanism at the museum of Athens ? If it is the former, how far is it from being complete ?
Sorry for the confusion, I was recently in Athens and saw the Antikythera mechanism in person. That said I'd love to see ClickSpring's version in person once it's completed!
From the same time period come the manually operated and far less complex Napier's Bones. Still pretty neat, and more likely what the 'average' person needing a calculating device would have used.
[1] https://en.wikipedia.org/wiki/Antikythera_mechanism