Wiktionary cites suck the oxygen out of as a variant of suck the air out of. The definition is as follows:
suck all the air out of
suck the oxygen out of
suck the air out of (third-person singular simple present sucks the air out of, present participle sucking the air out of, simple past and past participle sucked the air out of)
One meaning of "to mill" is "to move about in a disorderly or aimless fashion", especially in a circular movement. The "periphery" is the edge. So basically, the section is just stating that Hassan was in their life, but not in a purposeful or meaningful way.