"strutting down the street with a nine-stone canine pretty much says: ‘I’m so important that I don’t have to care about your feelings or your social standards.’"

It can also mean 'I'm a drug dealer. When you get mugged/your house burgled, that money eventually ends up in my pockets. Don't even think about complaining or me and my dog will hurt you."
It's a threat, but not a threat that you can complain to the police about.

Source: used to live in a really shit neighbourhood! 

 I would say both meanings are effectively saying the same thing, just to a different degree.