I encountered this phrase and after a bit of Googling, it seems to describe the action of crowding around a particular thing or object (people crowding around someone, trees crowding around a building) but doesn't 取り囲む itself also describe that action? Does omitting the 周囲 change the effect of its use in sentences or is it more similar to an idiomatic set phrase?
The sentence i saw it in was:
周囲を取り囲むように大勢の学生が集まっている。