I was reading Atul Gawande's Being Mortal, and the following sentence came up in Chapter 5.
If your dog is running the roost, it may not be such a good idea.
What does "running the roost" mean?
rule the roost
To be the real boss; to be the person in charge.
You just need to accept that your daughter is going to rule the roost for most of her childhood.
For all intents and purposes, it's the assistant manager who rules the roost.
In the sentence you provide it would imply that the dog's owner could not control the dog enough, therefore the dog was in control of them. A "roost" typically refers to a place where birds sleep and in this case refers to "the home."
"Ruling" and "running" can have similar meanings. To me "rule the roost" sounds more idiomatic because of the repeating of "oo" sound. Also at first I thought running the roost might mean the dog was "running [away from] the roost," but that does not seem correct.