My Checklist for a RPG.
Character Creation: I need to be able to create my character in some way. I dictate his or her skills, his or her abilities, and possibly his or her general appearance.
Character Development: I am not talking story aspects here, but actually having the character gain experience and power which increases his or her skills and abilities during gameplay.
Success and Failure are Character Dependent: The actions in which the player does succeed or fails based on the character's skills and abilities and not the players.
Simulated Dice Rolls: There needs to be a certain level of randomness and uncertainty.
Story Driven Interactions: The character should be able to talk to NPCs, gain information, develop in story, and they such. Interactions like this are key in proper story telling.
These are things that are just off the top of my head. If I think of more I'll post them.