walkitalkiさん、分かりました、ありがとう。

"swathes" is not always related to violence.

"<em>He owned vast swathes of farm land</em>" is possible (no violence).

My guess is that the journalist uses "watching terrorists seize growing swathes of Iraq" rather than "watching terrorists seize large areas of Iraq" because the journalist wants to describe terrorists taking useful, agricultural land.

So It means to seize a land by violence, right? 

A swath is a significant sized piece of land. It sort of implies that it was taken in a single strong movement.