I'm not sure I understand the question. If this game wasn't based on Star Wars it wouldn't be this game, but something else. The story-line and many quests would make no sense and the entire concept wouldn't be as appealing, considering how many of our emotional responses to all things Star Wars are hard wired in our psyche as a result of decades of exposure to marketing strategies well beyond the occasional add; we're talking big time, hardcore, top notch marketing here.
Would I be playing this game if it went under a different name? Probably, because I like the Star Wars universe and I'd realize the obvious connection.
Would I be playing this game in a parallel (and dystopic) universe, where Star Wars had never existed? It is impossible to know. Would you have liked the Terminator had it not starred Arnold schwarzenegger?
In order to answer with a straight 'yes' or 'no' one has to make too many assumptions based on nothing but speculative nonsense, which would ultimately lead to more nonsensical speculation that would soon spiral out of the control of logic and into the realm of surrealism.