"Runt" in this instance clearly means "throughout," but can it also mean "around" in the other sense of the English word?
Yes, the "around" meaning is the one most commonly used in sentences. For example "Hon går runt huset" means "She goes around the house".
So "runt" means more like "going around in circles" and "runt i" means "going around to cover more space"?
It could be a single circle, or just parts of one, but that's indeed the gist of it.
M.r Hinz i have heard many americans using...round ...for traveling trough but it was wrong here
'drives' is kör in Swedish, but åker here only implies that he is using some kind of transportation. He isn't necessarily even going by car, he might be taking trains and buses.