You are wrong, because even though an infinite loop occurs, a player will be at 0 life when priority passes in between the triggers, when that happens, a player loses the game. 104.3b If a player’s life total is 0 or less, he or she loses the game the next time a player would receive priority. (This is a state-based action. See rule 704.)
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Also, is this meant to be a Legacy deck? If so, it's illegal because Sol Ring is banned. If it's just a casual deck, never mind ;)
It actually causes an infinite loop with Stuffy Doll. So once its active, you win (barring a stifle, trickbind, or removal of some kind). Stuffy Doll does 1 to itself -> Guilty Conscience triggers dealing 1 damage to Stuffy Doll + Stuffy Doll triggers dealing 1 damage to chosen player -> Stuffy Doll triggers dealing 1 damage to player + Guilty Conscience triggers dealing 1 damage to Stuffy Doll -> etc etc etc.
This is a Legacy/Type 1.5 deck, so there is no restriction like in Vintage/Type 1. Yes, the win is either hitting one of the two Grapeshots, or grabbing a Brain Freeze (either with scroll or wish)
Where's the Guilty Conscience? Works way better than Pariah