If you want to understand how close Norwegian, Danish, and Swedish are, you might try listening to or reading Scots. Some consider it to be a dialect of English, but it is generally accepted to be its own language - having diverged separately from Early Middle English. I don't understand everything this speaker (left) is saying, but I'm fairly certain he's talking about the English-speaking school system correcting his Scots for being "bad English." 

The video description is inaccurate, or misleading at best: the speaker is mixing Scots and English - he is not just speaking Scots here. This is an example of how a closely related language gets confused for a dialect of the dominant language. This doesn't really happen with the aforementioned Nordic languages due to national boundaries as well as the lack of a dominant language amongst the three.

To hear Scots by itself, click here.

Norwegian, Danish, and Swedish are largely mutually intelligible, and their speakers probably have more experience trying to understand one another than you or I do trying to understand Scots - which no doubt contributes to intelligibility.

Similar to Scots, there is a little known language in Sweden called Elfdalian. Elfdalian is a Nordic language spoken by no more than 3000 people, and a Swede might tell you it's just a dialect of Swedish. However, it's actually fairly different grammatically, having retained some complex grammatical features from Old Norse that Swedish lost. Because of this, it might actually be further from Swedish than Danish or Norwegian. It's considered its own language based on lack of mutual intelligibility. Elfdalian speakers also speak Swedish, just as Scots speakers also know English. This creates the possibility that Swedes would be similarly confused, upon hearing an Elfdalian speaker, as to whether they were listening to Swedish or Elfdalian.