I don't think it's a fundamentally strange idea, just that almost all games fall so squarely on the entertainment side of the art/entertainment divide that they're just not applicable.
For me it's quite a high bar anyway. Far more films have artistic value than games, but it's still quite a small minority of all films. And only some of those films actually make me emotional. And only a small fraction of THOSE would actually make me cry!
Insomniac's Spiderman got me real good. The ending worked really well on several levels. To it top it all off by what I thought was an excellent take/twist on what usually happens to Peter in a lot of his origin stories
Some of the game was a little uneven, but when the game focused on the main threads of the story it worked really, really well.
Legend of Legaia on the original Playstation. The game had a very melancholic OST, and the adventure itself had some sad hints. I remember being very emotional when I defeated the final boss and the epilogue and end credits started to roll. Loved that game.