IIRC, technically if the vehicle meets emissions limits without a catalytic converter then it doesn't need one.
The emission limits are set such that a catalytic converter is required to meet them. They don't have to say "catalytic converter required" but the targets are chosen so that a catalytic converter can reasonably achieve them.
If the laws simply said "catalytic converter required" then manufacturers could put a tiny little square of catalyst in the exhaust and call it a day. Formula 1 isn't the only place where rules have to be written explicitly to avoid clever workarounds.