Question: How does the fact that Biff is wealthy in the alternate 1985 have such a dystopian effect on Hill Valley, turning it into Snake Plisken's L.A.? Someone's wealth would probably not have effects on crime rates, murder, schools burning down six years prior, etc.
Answer: While I don't think Biff's motivations are explained in the film (but maybe they are in other canonical material), it seems to center on the casino that Biff opened and the type of people it attracted. Biff also tells Marty he owns the police, which would indicate Biff was also engaged in illegal activities, for example prostitution or drug sales, and there was police corruption. This also seems to have increased gang activities (which Biff may have been involved in as well) that led to more violence and crimes like arson at the school.
Answer: Biff is so wealthy that he is basically an oligarch, ruling Hill Valley. As he puts it, he "owns the police," so he is above the law. He puts all his resources into his own life, neglecting the rest of Hill Valley. Without these resources, all of the services (police, health, education, social services, fire, etc.) are non-existent outside Biff's tower. Therefore, it sinks into poverty, lawlessness, and despair.