Click on the game content description to download an emulator replay file. A replay file is simply a recording of controller inputs per frame. This method allows you to watch a replay in lossless quality at a very small file size when compared to video, and also adds customization options (e.g. adjusted palettes, scanline shaders, etc.). You will however need to have a copy of the game ROM and the emulator used for the recording. Emulator downloads are provided, as well as links to the replays on YouTube for convenience.
If you're new to operating MAME through Command Prompt, read this.