what makes a game a game?

Today during discussion, gaming lab consultants (kids) answered the following question; What makes a game fun? The brainstorm session produced an informative insight on what motivates kids (of this age group) to play video games.
Here are the results:
A game needs to have a goal with rules and a challenge; the game must challenge the player with existing skills or teach new skills; a game must have a winner and a loser with punishment and reward incentives; and finally a game must be interacitve. The brainstorm session was positive because the students felt their perspective was valued. It made them feel like game consultants.
Eddie