I am not much of a critic and I am absolutely NOT a poet but I think your poem is very nice.
When I read it I immediately thought of the song "Everything" by Bread which, to me, is the ultimate tear-jerker. Part of that reaction comes from context - it was the song that my friend played at her young son's funeral.
Beyond that though, "Everything" is really all about the "you" person where your song seems to be more about "I". It is the "I-ness" of your poem that keeps me from having a really strong gut reaction to it.
Does that make any sense?
I really love this part:
I'd like to hear more about "that game". Maybe how the game helped to create such a bond between the two of you - the "not much"ness of the game is particularlly compelling to me.
Poetry is not a topic I am very good at so take my comments with a grain of salt. I think it is a beautiful and heart-felt poem. Thank you for sharing it.