I don't think there has been a game like that yet, if only because gaming as a medium is so, so young compared to movies. Citizen Kane was made long after movies had become an acceptable medium, and gaming is still only, what, 25 years old at most? We may get something some day that melts into the mainstream media and paves the way for the public to accept our hobby, and see it as the medium of expression that it is. So far, however, I feel that hasn't happened.
The closest I can come to something which qualifies is, to me, the Half Life series. Mainly because it, like Citizen Kane used many movie-techniques, uses a constant, interactive narrative rather than cutscenes. To me, a game cannot hope to possess the honour of being compared to Citizen Kane if it still uses movies instead of gameplay to tell its story. Half Life 1 and 2 are, to me, the best series to constantly show the world through the protagonist's eyes.
If you want to compare games to Citizen Kane, you must compare the usage of medium. Many good stories have been told before Citizen Kane, and many good stories have been told in games. But to rise above them and become something more, a game must fully use its medium, not borrow from others.