Doesn't have to be a different dimension, international waters or space would do.
Both those places are heavily government controlled.
In fact international waters if you're not flagged and registered to a specific country, then it's open season for anyone to board and seize you.
Aside from the counterpoints made by the other responders, this still won't work: you need a physical connection to those servers, and you can't just WiFi to servers thousands of kilometers away. So the servers need to be in another dimension, so you can access them without government interference.
All this, and no mention of Sealand [0]? An unrecognized micronation in (formerly) international waters, with a hosting company (back then) that allowed almost everything, and its own coup and counter attack by the "legitimate" royals (and then Germany having to negotiate POW release of the coup organizer).
[0]: https://en.wikipedia.org/wiki/Principality_of_Sealand