The book doesn't introduce any new rules. They simply emphasize a design philosophy that existed from the beginning. Open up the MM and go to "Death Knight." Now read the "Hellfire Orb" action. This spell-like magical ability is what everyone is talking about. MotM, and monster design moving forward, emphasis these spell-like magical abilities over simply listing a spell. There is nothing new here conceptually, they are just using this type of design on all spellcasters.
EDIT: Incase you don't have the MM, here is the Hellfire Orb from the Death Knight in the MM:
Hellfire Orb (1/Day). The death knight hurls a magical ball of fire that explodes at a point it can see within 120 feet of it. Each creature in a 20-foot-radius sphere centered on that point must make a DC 18 Dexterity saving throw. The sphere spreads around corners. A creature takes 35 (10d6) fire damage and 35 (10d6) necrotic damage on a failed save, or half as much damage on a successful one.