What kind of component was used in this demodulation circuit?
They are commonly known as IF (intermediate frequency) Transformers.

They can have various winding arrangements (tapped/untapped, single/transformer) - the 5 pin base is common, and are used for filtering and coupling.

In this case the filtering function is being done by ceramic filters (CFXX on the pcb)

The IF transformers are used as a simple single coil, LC resonant circuit used as frequency dependent phase shift elements for the FM demodulators.

There is a space underneath where the resonating capacitor can be optionally built in. That is the little brown ceramic tube.

The slot in the top allows them to be tuned onto frequency by screwing the ferrite cup over the coil.

Pull the metal case off and have a look inside.