I think you may be misreading the map from that link a bit because it is fairly low detail and doesn't point out the landmarks very well. The "gyre" as it is referred to in the linked page doesn't really reach the northeast US much at all, it mostly stops at around the area between NC and VA where the coast protrudes. If you want to see a cool image based on satellite data that shows it off, check this out (https://www.earthdata.nasa.gov/news/worldview-image-archive/gulf-stream). That being said, some of that warm water does still affect a the NE US a bit (not so much for Canada), so the gulf stream faltering will make it colder, just not as dramatically as places like the UK which based on latitude would likely have temperatures closer to Sweden and Norway.