An arcade cabinet, also known as an arcade/coin-op arcade machine, is the housing within which an arcade game‘s electronic hardware resides.

Arcade does not refer to the games or the cabinets they were/are in, it refers to the business/building that provides you with a place to play them. The etymology does indeed derive from a series of arches. The “series of arches” became common usage for any covered walkway, frequently one lined with shops or amusements