Often used in legal or formal contexts, such as the 風俗営業等の規制及び業務の適正化等に関する法律 (Law Regulating Adult Entertainment Businesses), where 遊技 refers to games like pachinko. In everyday speech, ゲーム or 遊び is more common.
Under this law, pachinko is classified as a game.
People under 18 are not allowed in game parlors.
slot machine
Compound of 遊 (play, amusement) and 技 (skill, technique). The exact historical derivation is uncertain, but it likely emerged in modern legal and industry terminology to refer to games of skill or chance.