This character is a Other Symbol and is commonly used, that is, in no specific script. The character is also known as video game controller.
The glyph is not a composition. Its East Asian Width is wide. In bidirectional text it acts as Other Neutral. When changing direction it is not mirrored. U+1F3AE offers a line break opportunity at its position, except in some numeric contexts.
The CLDR project calls this character “video game” for use in screen reading software. It assigns these additional labels, e.g. for search in emoji pickers: controller, game.
This character is designated as an emoji. It will be rendered as colorful emoji on conforming platforms. To reduce it to a monochrome character, you can combine it with Variation Selector-15: 🎮︎ See the Emojipedia for more details on this character’s emoji properties.
The Wikipedia has the following information about this codepoint:
A game controller, gaming controller, or simply controller, is an input device or input/output device used with video games or entertainment systems to provide input to a video game. Input devices that have been classified as game controllers include keyboards, mice, gamepads, and joysticks, as well as special purpose devices, such as steering wheels for driving games and light guns for shooting games. Controllers designs have evolved to include directional pads, multiple buttons, analog sticks, joysticks, motion detection, touch screens and a plethora of other features.
Game controllers may be input devices that only provide input to the system, or input/output devices that receive data from the system and produce a response (e.g. "rumble" vibration feedback, or sound).
Controllers which are included with the purchase of a home console are referred to as standard controllers, while those that are available to purchase from the console manufacturer or third-party offerings are considered peripheral controllers.