"Him" is actually referring to Gamzee. As far as I can tell, Gamzee is the only one who has caused Terezi to intentionally "damage" herself for his black love. If she doesn't become kismets with Gamzee, she'll have no qualms about killing him off on the asteroid in Act 5. And even if that's avoided, she won't end up chasing him in the events prior to [ S ] Game Over which ultimately lead to her death.

Stealing Pumpkinsnuffle won't have any effect on the game she's playing (the defendant is found guilty anyway), but since Terezi was able to smell John, she'd be able to recognize his interferences as the game goes on, to the point that he basically helps her out through her session so that she's fully prepared when they get to the Alpha Kids' universe. Heck she might reach God Tier with all of John's interfering, meaning that even in the unlikely event that she gets stabbed again, it won't kill her (since her death was neither just nor heroic).