While I can't confirm this as I haven't read them, I believe Assault on Arkham is meant to tie the Arkham games to the New 52 comic series. My only proof of this is what I've heard about New 52 and some of the lines in Assault on Arkham implying these events. That being said though, the movie faithfully replicates the Arkham Asylum from the Arkham universe with a bit more detail thrown in. Fans of Arkham Asylum will easily recognize iconic places from the game including the Penitentiary, the caves under the asylum and the Botanical Gardens. Even the designs for the characters fit the Arkham universe with Batman sporting Detective Vision, Commissioner Gordan, Joker and Riddler (to name a few) all having the designs either used or based on the Arkham games (the noticeable one for me was Joker's suit being different from his Arkham suit slightly (the tails on his suit).
The soundtrack for the film is well done, but nothing sticks with me. Like with the Arkham games, the soundtrack for Assault on Arkham flows with the story and is used to make the experience better. But as a result, its hard to recognize it throughout most of the film and when you do find it, its not a melody that you remember easily. It could just be that I need to hear the soundtrack away from the film though.
Would I recommend Assault on Arkham? Yes... if your mature. This movie isn't for the kids by any stretch of the imagination with several lines and shots being intended for older fans of Batman. However to be fair, the Arkham games aren't for kids either so if you're playing the games, then you should watch Assault on Arkham (if you haven't already). So what to do after you take down several goons and rouges? Hit the dangerous karting race tracks and lob shells at one another. Mario Kart 8.