With the exception of a couple of new mechanics,
Batman: The Telltale Series: Episode 1 - Realm of Shadows plays like most other Telltale adventure games. You will play through conversations with a limited time to decide on various dialogue options, and each of those choices can lead to differences in how the other characters feel about Batman/Bruce Wayne. While some of these choices don't seem to have any lasting effect, others could see larger consequences as each episode is released.
Action sequences are quick time events that, for the most part, feel right for the various moves that Batman performs. The game prompts you to tap an arrow key, Batman dodges in that direction to avoid an attack. If Batman wants to land a punch or kick, a keyboard key will appear. It's all about tapping out the keys the game prompts. Anyone who has played a Telltale game since The Walking Dead: Season 1 should have a good handle on what to expect from these sequences. The biggest difference I've found here, besides the occasional addition of the (Shift) key for a bit of extra umph, is that these combat sequences feel much more crisp, quick and efficient when compared to past games.
The closest Telltale game to have this level of combat in it was The Walking Dead: Michonne, but since Batman is a much more skilled and versatile fighter than Michonne, it shouldn't be a surprise that Batman: The Telltale Series kicks the combat up a notch.
As for the game's story, Episode 1 - Realm of Shadows has Bruce Wayne backing DA Harvey Dent for Mayor, while Batman is hunting a new burglar, Catwoman. When Batman corners the leather-clad thief, he manages to nab her prize off of her, an encrypted hard drive, and starts the process of decoding the device. Meanwhile, Harvey's desire to grab every vote seems to have put him in bed with notorious crime boss Carmine Falcone, and with Bruce also backing the DA, it could mean that the playboy billionaire has to deal with the kingpin as well.
Realm of Shadows does a pretty good job of dividing your time between both Batman and Bruce Wayne. On the Dark Knight side of events, Batman's investigations lead him to a gruesome crime scene where he has to use his detective skills to piece together exactly what happened. Here is where one of this game's features really shines. While investigating the scene, Batman has to link various details with others in order to get a clear and accurate picture of exactly what happened. In a similar manner, Batman later plans out an assault by linking enemies to various elements of the room, in order to plot out his exact attack pattern. Both of these aspects really help to convey Batman's more intellectual and methodological side.
Of course, while Batman has to track down mob bosses and gather information, Bruce's life isn't all cocktail parties. Apparently out of nowhere, the Wayne family is under a character attack as rumors rise connecting the Waynes to organized crime. As Bruce starts to track down exactly what is going on, he has to decide how much of his current problems are because he is backing Harvey in the election, or because he might have made an enemy in Falcone.