I don't think the writer of the guide understands what "Annex" means. But they do use the word annex.

"Laying siege to an opponent will not eliminate them, but it will give you the option of annexing their city."

A: Annexing would be cool.

B: It would never happen because of the amount of rage and butthurt people would be in might actually cause the forums to actually catch fire.

And I can see why. Having your city, especially a city that you might have spent real money on, be taken over by someone else opens way too many doors that the Devs probably aren't prepared to handle in any fashion.