In a video game, the player is the person responsible for operating the game through the use of the controller, or whatever other control schemes may be used for the game's operation. The player is a near constant presence in the world of video games, and is an extension of the role of the viewer in other forms of media. Unlike the viewer, the player not only observes but also has a personal stake in the events, due to having an affect on the outcome of the world. Being postmodern works, the Kill the Past games, along with other Suda51 and Grasshopper Manufacture games, will sometimes directly or indirectly acknowledge the existence of the player.
The player is asked for their name at the beginning of The Silver Case, which becomes the name of the protagonist of the Transmitter cases. The Transmitter cases are played entirely in first-person and the protagonist never speaks, which are common immersion tactics. However, The Silver Case deconstructs the concept of the silent protagonist by implying that he is literally mute. Those who don't know him, rather than seeing him as a stoic hero like other silent protagonists, see him as an intimidating and even frightening man. On the other hand, Tokio Morishima, the protagonist of the Placebo reports, is extremely talkative to himself/the player.
The role of a video game player is heavily paralleled by the personality and actions of Sumio Mondo. Sumio is driven to help out and find missing items for the various guests on Lospass Island, for often arbitrary reasons. Every single one of these searches is performed with the use of a computer named Catherine, much the same way that a video game player must rely on their computer to interact with the game's world. Sumio also needs, more often than not, the assistance of a manual/strategy guide, The Lospass. Sumio only breaks his calm demeanor when Shoutaro Kai, or other characters, insult the video game itself.
Similarly to the above example, Harman Smith and Garcian Smith's interactions with the world parallel that of a player. Harman Smith in particular is confined to a chair and uses the medium of television in order to communicate to Garcian. When on the field, and not playing as Garcian, it can be speculated that Garcian is using said television to control the other Smiths, hence why you must return to Harman's Room in order to switch between him and the others; this is supported by Hand in killer7, which states that Garcian is literally pressing a button on a controller to revive dead personas. Kun Lan also hints that he is aware of the player, as he says that the world can be controlled in the palm of your hand, "just like a PDA".
Contact has the most direct link between the game and the player, as the Professor converses with you regularly throughout the game. Terry being under your control is discussed by the characters, and the Professor wants to keep it a secret from him - when Terry finally does learn the truth, he calls you out on taking control of his life.
The 25th Ward suggests a metafictional approach to Kamui Uehara. He is described as "the main character of all of this", and as an omnipresence that can give messages to people, which suggests that the player, as a level above the protagonists that they possess, is the true nature of Kamui. This theme is continued through Kosuke Kurumizawa, who is also an omnipresent observer, but "exists within Kamui's power", hijacking it in order to attain his observer powers. Kurumizawa seems to be the character the player is controlling, as the cursor used for interacting with the world as well as possibly the running man used to select chapters are actually manifestations of him. By going between the player and the actual protagonists of the game, Kurumizawa is definitely hiding within the player's power.
The different approaches to protagonists between the two games also fits with the idea that Kamui's true form is the player. In The Silver Case, the protagonist is always either Akira or Tokio Morishima, and although some scenes are shown from unrelated third-person perspectives, those two characters are the only ones the player ever controls. Within Ward 24, Kamui Uehara is locked within the Kamui System and is controlled by the government as a "switch" that can be turned on or off, and consequently the player can only play from these limited perspectives. On the other hand, in The 25th Ward, Kamui represents chaos and isn't limited by the Kamui System (Uehara even states himself to be finally free from being restrained and locked away in the true final message of #07 black out), and thus the position of the protagonist is played with fast and loose, with eight different characters being controlled over the course of the game.
In No More Heroes, Travis Touchdown opens the game with a monologue to the player about the plot. Travis is consistently aware of the player's presence and views you as a partner of sorts, cheering you on when you engage in a clash and waiting for your command (pressing the A button) before beginning a mission. The player may also be what Sylvia Christel is talking about when she talks about trusting your Force. At the end of the first game, Henry Cooldown seems to know that Travis has your assistance as well, saying that both Travis and the player were likely expecting another plot twist.
Travis also represents the player, particularly the western one, in his love of video games, movies, wrestling and other nerd and otaku culture. He enjoys mindless violence and his initial motivation for becoming an assassin is to get money to buy games. His comments about the plot of the game reinforce this, portraying a cynical view of the average player.