There is a decent explanation here:
https://www.flight-mechanic.com/gyro...ating-compass/
Based on that I would say that you are mostly correct, but an RMI does not contain a directional gyro. The heading part of the RMI is derived from the flux valve. To break things down: a remote indicating compass is a magnetic compass that uses a sensor mounted outside of the instrument (the remote part) to obtain magnetic heading information and you can combine this with the ADF to get an RMI. This same remote indicating compass could also be combined with some other parts to form an HSI.