As I've actually helped certify a CAT IIIa system on an RJ (the Flight Dynamics, now Rockwell-Collins, Head Up Guidance System or HGS) maybe I can explain. This the same system as used on the dash8-400 and RJ-700 flown by Horizon.
In the 60s, most CAT III landing systems were of the Autopilot/Autoland type which normally needs a triplicated type of architecture to meet the reliability numbers. In the UK aircraft with this were the H-S Trident & BAC 1-11 using Smiths systems.
In the US, the Tristar, 747 & DC-10 all had Autopilot-based systems but, for the DC-9, Douglas collaborated with Sundstrand to certify a "hybrid" CAT IIIa system. This, in essence took a normal two channel Autopilot and monitored it via a HUD which also allowed the pilot to keep looking outside - making looking for the runway a much easier job.
Flight Dynamics took this idea a stage further and used data from the ILS and IRS to generate guidance that aloows the pilot to continue the approach to a 50 feet Decision Height (CAT IIIa). The pilot's performance - how close he is following guidance - is monitored by both the HGS Computer and the Co-Pilot using his instruments. Autothrottle is not required - or fitted - but speed control to within 5 kt is the hardest part of the task.
The turboprop you see is probably using a similar IRS-based system but for a different purpose. He is calibrating the ILS beam by flying down it to a known point on the runway. The inertial data is integrated to provide a record of the actual aircraft position on the approach which is compared with the beam data to see if it is within ICAO limits or needs to be adjusted.