The Game is the conceptual basis of the Welcome to the Game franchise. It's purposely ambiguous as to what The Game is exactly, although Reflect Studios confirmed it will some day be revealed. Obviously, the entire franchise's namesake refers to The Game, and The Game is clearly heavily involved with the Deep Web.
In Welcome to the Game, in the default ending, the final words spoken by Red Room operator The Executioner, is "I'm not doing this to you. The Game is doing this to you. Welcome to The Game!" before slitting his victim's, Larry, throat. This implies The Executioner's actions are in some way driven by The Game. Since he makes a living off his Red Room, this might mean The Game is in some way the "soul" of the Deep Web's depravity in some way. The business, the monopoly, the economy of the Deep Web and its inhumane content.
In Welcome to the Game II's ending, if the player tells Clint to sacrifice himself to save Amelea, the last words he'll hear are "Thanks for playing" from Adam. Adam is the leader of Noir and host of the Dead or Alive stream, just like how The Executioner is the host of the Red Room stream. This more or less states Adam is wrapped up in, or might even be behind, The Game, as a prolific, influential Deep Web operator.
There's also the obvious meta double meaning that The Game is literally the video-game the player is playing.