***WARNING SPOILERS***
I think that the game Grey is a metaphor for a one-sided relationship.
Every time he gives a gift, he become more transparent, which I feel represents loss of hope and/or faith. But, each time he gives a gift, he sees more, the blue sky, yellow flowers, etc. This, I think, means that he not just loses hope, but he also sees maybe another woman with a common interest, or a better personality. He starts to pay more attention to Woman B, while ignoring Woman A.
***LAST WARNING FOR SPOILERS***
I also believe that the grave is a symbol for the "death" of the relationship, a small memorial for the girl he thought he loved. The fact that he disappears obviously means they broke up, and the dove in Woman A's hands may mean that she found her actual soul-mate after the game.
I hate when people do this, but I worked hard on this, and I don't want this going to waste, so + if you agree