There is a finitely many moves at each stage: yes, at most for, at least two.
There is a finite sequence of moves that yields a solution: yes, move tile 1 on its position, then tile 2, and so on.
There are no chance or random moves: yes.
There is complete information about each move: yes, nothing is hidden, there is no fog of war.
Each move depends only on the present position, not on the existence or non-existence of a certain previous move: yes.