No, it's not. It's a judge enforcing a binding contract, an arbitration contract in this case.
There is a legal principle in contract law called "choice of law". Essentially, it allows for parties to establish what law will apply to the contract that they've executed. It can be a binding arbitration contract, a sales contract, a marriage contract, really any number of contracts have choice of law provisions in them.
For example, many wildly rich people will stipulate in their prenuptial agreements that a certain state's laws will apply in the divorce, irrespective of where the parties actually file for divorce. So, in a community property state like California, it wouldn't at all be unusual for a prenuptial agreement to specify that a more favorable state's domestic law would apply, like Florida's for example.
Virtually every international business contract that is executed in the US today, has one or several choice of law provisions in it; Maybe they're applying German law, or French law and sometimes when doing business with a Middleastern country, there is a sharia law provision. It happens.
It is NOT "sharia law invading the US".
See above - #22.
Make it #23.
You're no fun. Its much more exciting to see this as an invasion.
However, it does raise a question in my mind about the ability of our courts to understand and apply Sharia law and what must be many contextual interpretations that could be alien to our understanding of law.