A mirror game can only be interesting if some things are balanced to be challenging, and the focus placed on interesting game elements. As I see it:
The aliens win by successfully overthrowing earthling authority - by infiltration (especially in beginning when only scout ships can be sent) or outright display of force (a country openly surrenders from your battleships)
From their standpoint it's mostly management/strategy on how to spend resources : sneak in an advance base (resources, information, logistics), openly terrorize a hapless country (resources and a step towards victory), actively search those pesky XCOM (reduce opposition), study earthling brains in order to tune our psionic attacks (military perk) ?
Crushing XCOM or winning all major countries is victory, losing Cydonia is loss. But there should probably be an other condition of defeat, when earth defense "holds" and depletes all the resources the alien can send at them.