Arendelle could be part of a federal system, with an overarching government body extending across several kingdoms including Wesselton and the Southern Isles.
It's definitely a loose federation though, because each individual kingdom still trades with one another. They may not even share a common currency.
The question is: is the treason charge a local law or a federal one? Even if the legal boundaries are nonexistent, there is obviously a powerful church presence. If Arendelle has church backing, then they could press the charge past their own borders anyway.
It may also explain how the princess can give away power so easily and put an outsider like Hans "in charge" until she "gets back."
The local guilds and minor nobility probably hold the real power in Arendelle, suggesting that the title of Queen is more of a figurehead anyway. (The only official things she did as Queen was a party and an ice skating rink, suggesting she has a small Parks and Rec budget). These organizations, who obviously run Arendelle, would have a great deal of power outside the borders, and can use economic sanctions to enforce a cross-border charge.