I have to agree. Maybe it's because you're controlling the characters or because you feel a bond with them but video games put me in the story so much better than a movie for some reason.
And I'll have to try those two games Stargazer43. I too have a personal reason for liking the game (it was the final push that made me go get diagnosed. I had no idea about the story till after I was done). I even got a hold of the creator, Kan Gao, though very briefly.
But the story truly is what makes this game wonderful for me. It has that "Forrest Gump" feel to it, even though it's going backwards chronologically. And of course, if it doesn't have you in tears by the end of the game something's wrong.