They were the ruling class of half of England for a significant period. That is not marginal. It influenced laws, culture and language, though later displaced by the Normans who also had a profound impact. Were the Normans also marginal as they did not have a huge genetic impact?
That involved a rather genocidal approach in 1065 - killing everyone related to, or doing business with the Vikings. This tends to get downplayed by historians. And when the Vikings/Norsemen came back for revenge in 1066, King Harold 2nd managed to kill off the Viking force at Stamford Bridge, but was too exhausted when William invaded down south (being defeated at Hastings). 300-ish miles is a short drive by car, but in an era long before preserved food or mechanized transport, such a march over about 2 weeks would have been terrible.
Looks like Anthropic paid the Danegeld. Now they'll never get rid of the Dane.