The GameDex is a plot-central object in Video Gamer. It lists all the video games in existence and has to be filled up. The GameDex is a parody of the PokeDex from Pokemon.
In Ship Fighter, you play as a tiny white 8-bit detailed cupcake that the game calls a "ship" - a reference to how in classic games nothing looked like what it was supposed to represent. You fly around shooting bullets that look like forks at various evil cupcakes that are supposed to be UFOs. Every 37 enemies you beat you get a life and continue to the next stage, in which time speed is doubled. This continues for 10 stages, but by stage 4, the game is so fast it's hardly possible. The game in itself is easy, so if you don't think about it, you can shoot bullets like crazy and beat the "hardly possible" stages. By the 6th stage, the amount of ships is pretty small anyway.
To master this game you must beat all 10 levels.