Of course a city can enforce their own laws. The possible laws that LA (or any other city) could enforce against the video producers and vbloggers are many: zoning laws (enforcing laws against operating a commercial film set or business in a residentially zoned area); the requirement for an open burning permit, either all year or during times of fire danger; excessive noise ordinances, either 24hr or in a time span from late evening until morning; ordinances regarding excessive traffic and street parking; ID age checks for drinking, if police can get access to the property through warrant or other means; and investigations of criminal behavior shown in the videos.
"Basically, after today, if we film in this house we could face up to
six months in prison because we need permits," https://www.popbuzz.com/internet/social-media/jake-paul-banned-from-vlogging-in-house/
He could be talking about filming permits, traffic permits, burn permits, occupancy permits, etc.
Cities and municipalities can quickly enact new ordinances that criminalize behavior that impacts the neighborhood as a whole after taking into account complaints from neighbors and advice from police regarding activities of the problem residents.
Another aspect of the story is that it appears that Jake Paul is a renter. That means the city and neighbors can put pressure on the landlord to encourage Paul to obey the law; failing that, the landlord could possibly evict Paul in a very short amount of time due to possible damage and other clauses in the lease regarding illegal activity, if the lease stipulates anything like that.