An relevant discussion on the IGDA mobile forum about how to define a mobile game:

What exactly is a mobile game and why is there confusion? This may seem like a simple question, but there are many different opinions out there.

The schedule and sessions from this past GDC and Mobile GDC imply that mobile games are games to be played cell phones. At least, that was the topic of almost every session on mobile games. Haven?t we had mobile games for years with the Game Boy(s) and similar devices? (...) As we continue to expand into non-console mobile, such as cell phone based gaming, what elements of mobile console carry over to cell phone play, and what does not?

As for me, I think a mobile game takes advantage of mobility (= different context/places/location, integration of movement, different settings with regard to privacy/public display, connectivity/seamlesness...) to create challenging situations.