Arcade Controllers is a broad category that encompasses the vast majority of third party controllers that are used for playing arcade games, arcade style games or fighting games. <br>
Many USB Fight Sticks work nativly on Linux without much of a configuration. There might be need for a slight input remapping if they are a console version of a Fight Stick.
There are several predone kits to make your own PC connected Arcade Machine. They use standard USB interface to connect ot the PC and many times the same connector board as in the standalone Fight Sticks while the trackballs has a seperate USB connection that simulates a mouse.
There should not be any major issues connecting these with RetroDECK except maybe a controller remapping.