The reason the Imperial accent ended up being British is because the Star Wars films were primarily shot in the UK when it came to studio work. Almost all the actors used for Imperial bit parts were jobbing British ones. I dare say most of the non speaking Rebel parts were British as well.
Antony Daniels, Alec Guinness, Caroline Blakiston, etc. are obvious exceptions (being British people with Rebel parts).
The game is just carrying on the tradition of associating the British accent with the Empire.