I hadn't previously heard the term "FMS Approach" but I am familiar with "RNAV Visual Approach," which are issued only to air carriers.
It does remind me of the current RNAV visual approach procedures, but the AR is due to the 'tailored' approach part of the adventure.
The waypoints are at setpdown fix locations, with at/abv designators, which appears to add a quasi vnav to the RNAV approach.
With RNAV visuals, the FMS auto computes a straignt line VNAV path. I think that the legs may too short and outside of the FMS ability, especially the dogleg at ALPHI for the FMS to keep up with a VNAV solution. Perhaps this is why it is considered a tailored approach requiring approval to use?
I have also encountered differences in the ac/FMS performance with AT/ABV altitudes on waypoints on final. Another good reason for the tailored designation on the procedure.
I seem to remember in AUS, the international crews are/were not authorized to use the RNAV visuals.