SPOILERS:
I think what happened is that Abel (the guy) and Myles (the one we play as) are about to move in together after Myles divorced their wife, Diane, but Myles is being indecisive about signing the lease.
They have a conversation about how Diane didn't like Myles hanging out with Abel because they were in love/had hooked up in the past, and Diane had worked that out. In university, Myles and Abel hooked up in the locker room, and then they fell out as friends and didn't talk for seven years until Myles' wedding.
At the end, they reconcile and decide to move in together and give it a chance.
At least that's what I understood anyways!
Edit: Also all the puzzles are Myles thinking about the past, and not being present in the room with Abel. That's why the story only progresses after Myles has "thought through" (solved) all the puzzles.