Video games are often enjoyable because they task you with juggling multiple responsibilities at the same time (not unlike other parts of life). However, there are some games that focus on just one aspect of play.
Shooting games usually require you to navigate through the world as well as dealing with targeting and shooting enemies. On-Rails Shooters and Light-Gun games take over the movement and navigation side of things for you. You are left with the task of targeting and shooting the enemies as they come into view.
These can be classic shooting games, tailored for an on-rails experience. Sometimes a stand-alone game, and sometimes a special edition of an existing franchise. Games like Point Blank, Until Dawn Rush of Blood, House of the Dead, Dead Containment and Dead Space Extraction.
This can also be games with shooting style targeting that aren't specifically about shooting. Games like Child of Eden, Rez Infinite or New Pokemon Snap. Or games that use targets as part of a skill challenge like Osu!, Pianista or Elite Beat Agents.
This list includes 2 games from the last 14 years, with 25 likes. They come from a range of different genres and play-styles and are all good games if you want to focus on targetting.