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// FlyingAs this creature transforms into Shinryu, choose an opponent.Burning Chains When the chosen player loses the game, you win the game

So, your opponent can still win via cards like Approach of the Second Sun or Thassa's Oracle, and your Lich's Mastery has no say in anything

Additionally, if you were to equip a Tearlaments' Monster, then during the End Phase when Pin Baller returns itself to the Extra Deck, the Tearlaments' Monster won't trigger if sent to the GY because the effect to return itself to the Extra Deck wasn't an activated effect

Its positive loyalty ability allows you to venture into a Dungeon and its ultimate ability gives you a major bonus for each Dungeon youve completed