Clearly they did have it:

"talking about our future. Plan a holiday together, exchanging house keys, fantasising about living abroad together for a few years"

"I made it clear many times that I'm serious with her, I am done fooling around"

Also, obviously, they have a sexual life now, and they regularly spend the nights together. So unless you expect people to always specify separately that it isn't an open or polyamorous relationship....it should be obvious that it's supposed to be an exclusive one.