Yeah, her back to you pretty much puts you out of the conversation. Even if the other person looked up at you, the girl between you would have likely interpreted that as looking at her, or similar. This would've made it easier to have the type of conversation you described.
This is one of the reasons Richard and I stopped going to the dinners that a group we are part of would have each month. We always felt like outsiders, stuck with resorting to 'listening in' for our socializing. Blah.
Yes, something that holds our attention instead of turning the attention onto the other person. Talking and joking gets done as a peripheral activity, not as the main focus. Walking is the closest i can come to giving someone attention, but that is because the physical movement relaxes my mind. Though walking in a noisy area destroys my abiliy to listen/hear/focus. But like, I am seeing the value in knitting circles. But usually prefer something like ...say...going to a park to listen to a band. The band has the primary attention, the talking comes in spurts. Or playing a game...the game has the primary attention, but there is still socializing happening. Taking a class together, as well. And so on.
My understanding of quality time is that the other person has your primary attention, and they have yours. For example...one can be shooting hoops with a buddy. But if that buddy has you as their primary focus, they'll be standing around, holding the ball while they talk, wanting your attention on them personally rather than on the ball, etc. This would be a mismatch for someone who wants to focus on the more hands on activities involved, or who uses the ball as a way of
decreasing the pressure to hold their focus on the other person.