No, Doki-Doki literature club is not a video game. It's a video storyline with participation. And it's dangerous to do so. It starts with a school dating club and a character to identify with just wanting to impress by writing poetry. It's free to play, so horribly easy for kids to get hold of. The innocent start soon turns sinister with references to violence, self-harm and even suicide.
I quote a recent player "I can't believe that the anime Narutaru with its super cute and lighthearted opening just did a Doki Doki and had a guys head cleaved in half by a monster in front of his sister. And then having it shove a spike up her you know what."