A terrifying ability worthy of a villain.
Once Professor Z decrees it as his “Rule,” it must be followed by whomever it targets. Nothing in this world is beyond his reach. The target’s agency is otherwise unaffected. They may loathe it, curse Professor Z’s name, and scheme about their next move, but the established Rule will be followed.
To even subtly resist Z’s Rule would take immense willpower, and even then for only an instant. What could you accomplish in such a short moment of freedom? Would it perhaps be enough to turn the tide against him? Maybe so.
What weaknesses does such a broad ability have?
For starters, the more targets there are, the more mana the ability requires to keep the current Rule or Rules active. The number of Rules also affects how much mana is used, as does the broadness of a Rule. Something as specific as “you may only use a certain kind of Pokémon” is easy to use, but a Rule like “you may not oppose Professor Z” would take a substantial maintenance cost.
There are other weaknesses of course. But certainly you can figure those out, right?