I'm not sure whether it truly supports dual core.

Armies that my old single core laptop would display (i.e. 1 full stack on either side plus one fullstack enemy reinforcements) are refused on my new dual core one, saying how my hardware is not good enough (although its really double as good as before, not only in processing power but also graphics etc)

So no, I don't think 1.2 has proper dual core support. As for Kingdoms, the readme posted on the forum does not state anything about dual core support.