The US (and Canada, where I live) has an extradition treaty with Romania.

The US treaty does mention that

...neither Party shall refuse extradition based on the citizenship of the person sought.

But I haven't read it in detail so that may or may not be relevant (the past I quoted is referring to a particular part of the treaty).

My understand is that typically the threshold for extradition is mutual criminality which I suppose is my answer to how US law applies itself outside US territories (because leaking state secrets is a crime in most countries). So I withdraw my inquiry.

If Romania declared Borat a state secret pirates could perhaps be extradited.

But also note that I don't think Assange can be charged with treason, because he isn't American.