To "chug" is to drink your beer in one go. This matches the gesture, which could be miming the act of lifting a glass of beer and "chugging" it. This is generally considered to be juvenile behaviour, typical of young men in student fraternities. You can imagine a group of students, one is drinking and all the others are telling him to "Chug! Chug! Chug!"
It seems that the comment that is being made here is that the young Senate candidate looks like a student fraternity member.