Everything in this case could have happened identically in the US... because nothing here was actually out of the ordinary.

This was a legal arbitration that both parties agreed to. The arbitrator made a decision. One of the parties then completely reversed their previous consent (because he lost a shitload of money) and declared that the arbitration method of a sharia court is an inherent violation of Austrian Law. The court found that his rights under Austrian law weren't actually violated, so the decision stood.

I agree that Sharia Courts should be banned even from arbitration because the Sharia courts inherently violate the liberal principles of the US, but excluding that, this process went exactly as it should within the letter of the law. You can not agree to an arbitration, then declare the entire mechanism of arbitration to be incompatible with justice, just because you lost.