'Top-down' and 'bottom-up' as adjectives imply a directionality.
In the workplace, we might say some project is planned from the 'top-down' as meaning the same as "dictated from higher levels of management" or "centrally controlled", whereas a project planned 'bottom-up' is the same as "designed/planned by the users or lower-level employees" or the like.
You see similar language in newspaper discussions of political parties, e.g. "The party is neglecting its grassroots by rigging the primary in favor of Candidate X, and leading from the top down is sure to breed resentment." etc.
This particular passage is from Robin Hood, and in this context what they are saying is the system is corrupt, starting at the top (the King) and down through his agents (in this case the Sheriff of Nottingham).