The final grid numbers 1 through 9 also represent the unit height (e.g. storeys) of the building sitting on each cell. So in true Skyscraper fashion, the outer numbers provided around the grid indicate the number of buildings that are visible when viewed inwardly across, up or down the respective row or column, or diagonally from the four corners.
Have fun with this one! It's tougher than it might first appear! (Hint: Some digits will be duplicated along the two diagonals, so this isn't a Sudoku 'X' problem!)