“Arcade” comes from the Latin arcus, “bow” or “arch” (the same root as arc), by way of Italian and French. In architecture it originally meant a row of arches supported by columns or piers, the kind you see along cloisters, Roman aqueducts, or the front of old European buildings.

The meaning then shifted in steps:

  • Covered walkway. An arcade of arches along a building makes a sheltered passage, so the word came to mean the walkway itself.
  • Shopping arcade. In the late 1700s and early 1800s, glass-roofed passages lined with shops became fashionable, such as the Paris passages couverts and London’s Burlington Arcade (1819). “Arcade” came to mean a covered lane of small businesses, and the word still has this sense.
  • Penny arcade. Around the 1890s–1900s, venues filled with coin-operated amusements appeared, often in or styled after these shopping arcades. They had peep-show viewers, phonographs, fortune-telling machines, and strength testers. In the US these were called “penny arcades,” and in Britain “amusement arcades,” especially at the seaside.
  • Video arcade. These venues kept adding whatever coin-op entertainment was new: pinball in the 1930s, electromechanical shooting and driving games later on. When coin-op video games arrived with Pong (1972) and Space Invaders (1978), they went into the same places. By the early ’80s the video games dominated, and “arcade” became shorthand for a video game arcade. “Arcade game” then came to mean the style of game itself.

So the path runs from arches, to a covered passage, to a passage of shops, to a place of coin-op amusements, to video games. The architectural meaning is entirely gone from the modern sense, and only the “place of coin-operated fun” part remains.