A new part of the intro sequence is conversation between The Player and a Guard. However, the guard (and the player) start talking about the player having a girlfriend and going home every night. What's going on?

I think they were talking to another Guard. Personally, I didn't notice this until Omniary mentioned it.

The conversation is between the guard and the other guard behind the player. Though that's only made clear in one of the possible chit-chats they can have.

Alright, that sounds logical

Generally I find it a nice idea to add new voiced content in the beginning. The conversation about the girlfriend is, however, at my opinion a distraction from the kafkaesque tension the game builds up right from the beginning. For me it isn't a believable conversation in this environment. Just my two pence. ;)