In the US, at least, dogging basically means "to doggedly pursue", but used only when someone/something is being tracked or followed. I just looked it up in the dictionary (it is the definition for the verb form) to make sure it wasn't regional slang. The term originally meant sending the dogs after someone, really similar to "hounding", though "hounding" transitioned into more figurative usage while "dogging" remained literal.

In fairness, I think the term is rarely used today, but was much more popular in the prewar era when people were largely more familiar with hunting dogs. The only reason I know it is because I read it in a John Dos Passos novel and looked it up.