The shutter rate (coined by dpreview editors afaik) is the time it takes for the camera to expose and read the entire sensor in electronic shutter mode, it is different from the "shutter speed" which indicates the duration of exposure of each photosite and can be thought of as the "sync speed" of an electronic shutter as well as the fastest shutter speed at which no "rolling shutter" artifacts are to be expected (though not guaranteeing motion freezing).
Of specific interest are the Fujifilm X-T2, X-T20, X-T3, X-E3, X-H1 and X-100F as well as the recently introduced full-frame mirrorless cameras from Nikon Canon and Sony.