From a Boeing sim instructors point of view and from the recent airlines I have worked for, if a common garden variety flameout occurs (ie something turns off the fuel supply for some reason) it should obviously be considered an engine failure.
On the other hand if, quote " Fire is detected in the related engine; severe damage which may be associated with airframe vibration and/or abnormal engine indications has occured; or the engine has separated" then that is (in Boeing parlance) an "Engine Fire Severe Damage or Separation"
Put very simply, if you lost an engine because the N1 stopped, it would have been precipitated by a very short period of very severe vibration as it ground to a very painful halt. That is severe damage. Idunno, I would suggest that you did have a short period of vibration, you just missed the cues whilst trying to keep the machine under control. Not a criticism, it is just an observation from many hours in the sim.
If N1 or N2 stops (which it would do with quite significant vibration), if fire or overheat warning occurs, if airframe vibration occurs associated with loss of thrust or abnormal engine indications (which could be caused by accessory gearbox failure, loss of oil pressure, or loss of a blade somewhere, for example) , or your engine has departed your airframe then carry out the appropriate checklist that isn't an "engine failure checklist"