An arcade was a gaming establishment.
The full name of Quark's establishment on Deep Space 9 was "Quark's Bar, Grill, Gaming House and Holosuite Arcade". (DS9: "Profit and Lace")
The USS Enterprise-D had an arcade onboard, where players could participate in laser duels. The eastern portion had a forest in it. In 2370, Jake Potts and his brother Willie were playing in the Enterprise-D's arcade when Jake decided to prank his brother into believing he'd killed him with a real laser pistol, rather than the fake one they were using for the duel. (TNG: "Brothers")