I will first admit that I don't know much about alternate reality games, so I'm not entirely sure what different forms they can take and so forth. So from what little I just read, let me just say this first:

The game must be playable using a Windows computer.  No other devices can be required. And no other software besides the actual game files can be required. It must be a stand-alone game that can be played using only a computer and the game files. Also, if you have time lockouts as I see some ARGS do (like you can't progress until the next day of real time), you are likely not to get any judges playing very far into the game. The judges are busy people, and are not going to spend a week playing a game because they keep getting time locked out of it.

Other than that, a game that tells a story through the solving of puzzles certainly sounds like an adventure game to me.