By "all different polyomino sizes used in the grid are given", do you mean "appears as a clue in the grid" or "given on the outside of the grid"? There's no list on the outside for the example, but it might be the case in the actual puzzle.
It means the former, i.e., it appears as a clue in the grid. If a 2 isn't seen in the presented grid, a 2-sized polyomino cannot be used in the grid. Hope this is clear now.