If they had no cards in hand, or only one or two other cards, then theyre either guaranteed to discard the character you bounced back, or are getting rid or something equally valuable to them
For three mana, in White and Black, Anguished Unmaking can exile any non-land permeant at the cost of three life
And once youve slowed down their board development and you have enough mana rocks to break the symmetry, Armageddon will stop your opponents from interacting at all for several turns, while you continue to build toward a win
Jeff does a great breakdown of the deck in his gameplay video, so Ill just paraphrase his analysis
(1) Ritual Summon 1 Black Chaos the Dark Chaos Magician or Black Luster Soldier Soldier of Light and Darkness from your hand, by Tributing monsters from your hand or field and/or banishing monsters from your GY, whose total Levels equal or exceed its Level
If your lifegain deck struggles to close things out, you probably need more payoffs