The protagonist of DARK is Eric Bane, a guy who was bitten by a vampire and lost his memory. Unfortunately his "benefactor" is unknown and if Eric does not get to drink his blood soon, he'll become a mindless ghoul. So he sets out to search for rescue and his identity - the starting point being to seek out powerful old vampires whose blood could also work. The story is told in cutscenes and multiple-choice dialogues.
Despite receiving some vampire powers, Eric is weak and does not stand a chance in an open fight. So he has to use stealth tactics to overcome his enemies - basically he needs to break the line of sight by using cover (shadow plays no role) and approach unsuspecting enemies from behind to kill them silently. He does not use weapons and can't interact with the environment, so his only help are the already mentioned vampire powers: the two basic ones are shadow leap (similar to the blink mechanic in Dishonored, it allows to instantly teleport to another place in reach but has a short cool-down time before it can be used again) and vampire vision (shows enemies through walls and slows down time). All other powers, e.g. distract enemies or a big leap towards enemies in order to kill them, have to unlocked respectively upgraded with experience points and cost blood to use. Blood is earned by sucking out enemies, but this procedure is long and loud.
Of course there are also a few advanced obstacles to overcome, e.g. security cameras, light generators which disable Eric's powers or armored enemies which can't be sucked out. Enemies become alarmed if they stumble over corpses, so those can be pulled away to a suitable location. Unlimited free saving is only available on easy difficulty; normal only allows two manual saves between checkpoints.