I think a game can potentially cross over into the realm of art, when
the game in question has "meaning." For instance, the game of Pelota
in Mesoamerican cultures had a religious significance as well as being
a form of entertainment. Hunting or combat is often practiced as a
game, yet it also marks a warrior's transition from boyhood to
manhood. The Egyption game of Senet marked the passage of the soul
through the Underworld; success/failiure in the game predicted one's
success/failiure in the Afterlife.
If a game figures into the broader importance of our social
actions, or appeals to our sense of mythology, then I think there is
potential for a game to become Art. But I think a game taken by
itself is "just a game."
Spoken like a guy with a BA in Anthropology. :-)
Cheers,
Brandon