Provided that a full survey has been completed then the only reason why I can think a flight check would be required is to check the signal quality and track guidance provided by the navigation aids used to define the required track (if any).
If this was a standard approach and missed approach procedure doesn't the faa require the aid and the procedure to be flight checked on a regular basis?
Thus the FAA are not requiring any OEI take-off procedure to be checked - these are purely the responsibility of the operator. They are requiring that this new approach procedure and it's associated missed approach be checked in the same way that believe all approach procedures are checked before publication.
The OEI take-off procedure has nothing to do with it.
Regards,
DFC