YI'd have been happier with the truth, that the Klingons aren't fleshed out as well as the Federation is in "official" Star Trek lore. It makes it harder to add content for them, based on the series/movies. However, this is an alternate timeline. Wasn't the point of that so they could add content that was "out of sync" with the series and movies without disrupting everything?
This being an alerternate relaity from the old, there should be no real limitations to what they can add so long a they follow the basic rules, such as Starfleets Prime Directive and such.
Actually, it's the original time-line, however it's years after Spock and Nero went to the past, thus leaving our time-line and creating the alternate time-line. You are correct, though that they chose to have the game at this point in time to be able to add to the canon instead of being restricted to just repeating it.
As to your other point about lack of Klingon info in the movies and series, while this is true, there is a lot more in the books, which is also part of the canon.