Endurance charge on melee stun(ECMS) with phantasms/spectres/minions

Does ECMS more damage per endurance charge affect the damage of non-melee attacks/spells skill of the minion, if the minion has a melee attack skill. e.g. Half-remembered Goliath has a melee attack and casts spells. Would the spells be affected by ECMS more damage?

Yes, 4% more Damage per Endurance Charge applies to all damage. Minions don't even have to be melee (main condition - the gem shows it's supporteable by ECoMS). If you make them to get endurance charges in a different way, they benefit from the more damage stat.