"The game is based mainly around shooting and is viewed from the first person perspective, and someone should really come up with a name for that."The First Person Shooter is a popular form of Action Game. Its basic style of play is exactly what the name says: the perspective is first-person, through the eyes of the player character, and the action revolves around shooting. Contrary to popular belief, it's not always about shooting the first person you see. This is a game genre that was first widely popularized by id Software via Wolfenstein 3D. It actually had two potential sets of progenitors: there were games with a first-person, but not quite 3D because it was rendered in discrete steps, view of the surroundings, typically a dungeon (such as Ultima Underworld), and which had sensible and consistent worlds, NPC interaction, relatively few artificial restrictions, plotlines, and puzzles. And then there were games such as Wolfenstein 3D, Doom, and Duke Nukem 3D which had full freedom of movement but used it solely to let you shoot everything and proceed to the end of the level. Game designers went with the latter for a while, but as technology advanced, the genre has begun to shift towards having more interactive surroundings, setpieces, friendly NPCs, vehicle driving sections, physics-based puzzles, cover mechanics and RPG Elements with games like System Shock, F.E.A.R. or Half-Life. See Also: Standard FPS Guns and Fackler Scale of FPS Realism, Some Third Person Shooters have similar gameplay. Contrast Fixed Camera (in terms of perspective).
Examples of this genre: