G'Day Bartman !
Interesting questions there fella ..
To my way of thinking, the machine was kind of a mechanical means for documenting (and repeatedly generating) the observational data. Perhaps they chose a mechanical means to document it, rather than words and maths, because these means may not have reached the inventor's intended audience too well at the time. I wonder how many folk in those days would have understood a maths equation ??
It also predicted lunar eclipses etc, and the olympic years.
The device obviously came about because of observational data obtained by looking at the planets/stars etc. What was lacking in those days, perhaps, was the theory to explain the movements of the moon, planets etc. Whilst the machine may have gone missing, the data about the movements obviously remained for anyone who cared to look at the night sky and write the data down.
It took, perhaps, another five or six hundred years to develop the theory (if we use Kepler or Newton) to develop it.
I guess I don't think its loss would have made all that much impact on astronomy.
I reckon it would've made a big impact on the clock-making industry, maritime/navigation and, perhaps, the analog computing worlds, though.
(Just my 2 cents worth)
Cheers