Please offer some advice.

That is not true. If the Hero-owner of the Creature of Doom has this ring, then the Creature of Doom will attack with maximum force. I checked this. Also, instead of the Creature of Doom, it's an Angel, and instead of the Titan, it's a Devil (Amulet of Life). The ring works against skills and amulets obtained through the magic of LIFE. (The Amulet of Necromancy (Magic of Nature) works regardless of whether the ring is present or not).

The check is simply incorrect.
The Titan and the Devil have an innate amulet, so the Creature of Doom will always attack them "the same way," in the sense that it will be the same with or without the ring.
But in any case, the ring ignores amulets when the hero casts spells, not when dealing physical damage.

This cannot be, because read the description of this artifact: When casting spells, all amulet restrictions of creatures will be ignored, whether they are spells or abilities.
And now, WHERE HAVE YOU SEEN A HERO HAVING AN AMULET AS AN ABILITY???

Perhaps I was misunderstood.
The point is that the ring allows you to ignore amulets, both innate and cast; it doesn't matter who has this amulet, the hero or the creature.
It is only important that the ring works only for the hero, for its owner, but not for its army.

And an amulet for a hero as an ability is actually very common; for example, the Paladin, and there are also Armor of Life, Death, and Order - with their help, the amulet also becomes like an ability, not a spell. But that's not what we're talking about