If I understand the British definition properly, the same area would be referred to by Americans simply as “the pumps.” As in “Oh gosh, some idiot sick with Captain Trips just hit something so now there’s a big fire out at the pumps!” or “Dammit, there are about 12 cars at the pumps right now. I don’t have time to wait so I’m going to need to go to another gas station.”
Yeah, we would just use a descriptive phrase—“out there where the pumps are”—it’s seldom we have to be so specific about a particular area at a gas station, so I suppose we haven’t bothered to come up with a word for it.