The Visual style is called 'Str8nime' (Pronounced Straight-Knee-May) and is a combination of Anime (Much like Blue's animated style) 8 Bit Animation (A Throwback to the old Super Mario Bros. Video Games from the 80's in visuals as well as music) and Strangeness (Essentially the whole movie).
It takes place inside a lonely video game cartgage located on the floor of an arcade. The game is a ficitional grim/dark world which is populated by pastel puppets, paper dolls, toy dolls, 8-bit animated figures, & CGI people.
Unlike a Game Boy which is handheld, an arcade is stationary so Blue can easily play the arcade game better with both of her hands, even if she doesn't know the controls for the game.
In reference to HIM, the villain's dialog is based off of video games. The one notable example is the line: "Beware, I Live" from the cult classic arcade game "Sinistar." The other is perhaps lesser known except to those who owned a Sega Genesis in the '90s, is the line "Welcome to Your Doom" from the game "Altered Beast."