If this is completely false, as I imagine it may be with my lack of knowledge regarding ancient economies, what can they better be described as being?
Ask yourself this. How would you say current economics functions?
Is this a valid question? Is their only one way? North Korea and Hong Kong have radically different economies, but the are both around today and stable in their way.
Ancient times has lots on lots of different empires, nations, tribes and so on. Some were more like modern capitalism, other totally different. You should consider asking question that is a little more specific. However, their are were some similar questions, see:
This might help to get you started.