The way a player interacts with the game
The mechanics of a puzzle piece, or a game as a whole, are how the player interacts with them. The are closely tied to the qualities of the pieces, yet a distinct aspect, in-so-far as how one designs a game.
The mechanics determine how the player will solve the puzzle device. The mechanics are not abstracts, but concrete manners in which the player can solve a puzzle.
For example, in constraint logic, the player must take a series of statements are derive a single state. That is an abstract statement of the puzzle. In the concrete, the player will probably plot a series of dots and crosses on a grid, codifying their knowledge in a more useful form.
How the player tests their answer is also part of the puzzle's mechanics. Do they type their answer into a box, look at a screen and speak it, or spin some dials on a wall?
Assume everything in this reference is a working draft, there's prone to be some mistakes and inconsistencies. I figure it's best to publish and get feedback rather than write for years in secret. The terms will change, the structure will shift, and the bugs will be chased out. It'll take a while.