No, this claim is completely false.
For starters, Sebastian Kurz is not yet chancellor. Although his party won the election and has been tasked by the president with forming the next government, his talks with the other parties about forming a coalition have not yet concluded, and in theory he could, as part of a coalition agreement, let someone else be chancellor. Also, all talks could fail so he could not form a government at all, in which case the president might task the party in second place, SPÖ, with forming the government instead. Both these cases are extremely unlikely, but the point is that calling Kurz chancellor is currently wrong.
Source: kinda hard to find an article explicitly saying that he isn't yet, because that's so obvious to Austrian people. Here's an Austrian mainstream news source posting speculation about the final government. The article was published Oct 20th, two days ago.
For the concrete claim in the article, MediaMatters has debunked it quite thoroughly:
If the bombastic quote attributed to Kurz seems eerily familiar, it's because it was lifted word for word from a 2009 Rolling Stone article written by Matt Taibbi:
Beyond this, a Google search for "kurz soros" turns up the following kinds of results:
- Articles similar to this one by Der Standard that are about a different piece of fake news that came up during the campaign: that Kurz was sponsored by Soros and was his pawn.
- Reposts and translations of the yournewswire article, in various languages.
Notably missing is any reputable Austrian news organization picking up on the yournewswire story. You would think that such a decision would be published in our own news first. I've also tried to search specifically for articles in German, but all it turns up is stuff about the other Soros issue, and translations of the yournewswire article on private blogs.
Update: Austrian newspaper "Der Standard" has picked up on this new series of articles about Kurz (yes, apparently yournewswire published some more after the initial one). Unfortunately, their article only summarizes the articles and condemns them as fake news, but does not provide any new sources for the refutation.