On many modern aircraft the Advisory system is also sensor based, while the Primary Ice Detection system is typically automated and will activate EAI and WAI as required with no input from the crew. What the MMEL says here is if your Primary is out, there must be SOP to mitigate the loss - eg, in this case, more involvement of the crew. The category gives you an idea of the implied necessity of the system involved, with D category getting more time to correct than C.
In either case, while the MMEL does not specify the obvious, the crew will revert to visual and TAT methods of ice detection, use forecast data and PIREPS, and activate AI as per their SOP.