TOS and TNG were both within the Federation. Complete with trips to Earth, Vulcan, etc.
Here the Federation got blowed up, so we have to leave and find someplace else to live.
Hence, 'almost exactly', I suppose.
It's not a direct analogue, but in terms of what it allows them to do with the setting, it's similar. Even leaving aside that the Enterprise D explores areas of space the original NCC-1701 never touched, the Alpha and Beta quadrants were a very different place by the time Picard set out on his continuing mission - as were the civilisations that occupied them - and the gap in time between TOS and TNG allowed them a great deal more storytelling latitude than they would've had if they'd set the series only a few years after Kirk's five year mission.
The motivation behind setting this new game in another galaxy, a few hundred years after the events of the original trilogy, is similar, I suspect--with the need for added story flexibility further compounded by BioWare's laudable reluctance to canonise a given series of events in the original trilogy.