Intrinsic motivation
Also said as Playing for its own sake, Internal motivation
Doing something because the doing is the reward. Nobody plays tag for the points.
It is what is left when the rewards run out. A game with none of it loses players the day the unlocks stop, however generous they were.
Say it
“Before we add any rewards, test the core with the score hidden. If nobody wants a second go at the jump with no points, a points system will only hide that.”
Where you’ve seen it
People spent hours in Minecraft's creative mode, which has no goals, no score and nothing to unlock.
Not to be confused with extrinsic motivation
Intrinsic is wanting to do the thing. Extrinsic is wanting what you get for doing it. Most play mixes the two, and the same activity can move from one to the other.