I've been playing through Dark Souls recently, and I think it captures the ambient presence discussed in the article very well. You see ghosts of other players flickering in and out of existence. You can communicate with others by leaving messages, and you can view their deaths. A bunch of pools of blood left by multiple player deaths will draw your attention and warn you subtly that there's danger ahead.
But the actual multiplayer is constrained. Your offers of help can be accepted by anyone. You can be periodically invaded. There's no communication other than by movement and gestures.
It does feel like the gaming equivalent of sitting alone with other people. You're aware of them, can interact if you so choose, but your experience is still your own.