Imagine that you are standing straight and tall. Now look down at your belt buckle (or cell phone!). Rather than being in line above your feet, pelvis and shoulders, you let your head go forward.
Women sometimes "drape" themselves over their partner because they not only have their arm over the man's shoulder and behind the head, but allow more than a minimum of weight to be on that arm and their partner.
"There is a certain amount of butt visible on both sides."
The "forward lean" can/should come from the ankles and/or the knees. If it comes from the pelvis, the booty can be more noticeable.
This style comes from the center of Buenos Aires where milongas were crowded. Cacho Dante went their to dance because in the other parts of the city in his day mothers accompanied their daughters to milongas to keep an eye on them. With limited space and respect for other couples big flashy moves were not welcome.
"Clean lines" and how things looked to observers was unimportant.
What is important is the connection between the partners.
Dennis and Tyree aren't doing much with the music. Maybe I'll just leave it at that.