A commercial departs and suffers an engine failure. There is no immediate danger. The crew are well practised, there is no fire, and ample power to continue safely on one engine. The aircraft is not in serious or imminent danger but the crew call a mayday because they rightly require complete priority to return and land - it is SOP.
FUJI, No. Another case of the uninformed posting on matters outside their expertise, I fear...
Engine malfunction without fire in a CAT aircraft would require a 'Pan' call. One exception would be if it occurred in a State which may not recognise 'Pan' calls, in which case that consideration alone would dictate a Mayday. And it's not 'SOP' either, but trained custom and practise (I'm not aware of any companies publishing SOPs which are prescriptive to the extent of dictating specific declarations of urgency or emergency for specific conditions).