EME is the standardized specification on the browser side... That's all it is.
CDMs could technically only work for one browser via fingerprinting, but that could already happen without EME (or DRM entorely) using browser fingerprinting to only serve content to UAs the publishers "trust".
IE, firefox cannot use google sandvine, even if you have chrome installed, because it is not a standard interface from the browser's perspective.
CDMs are absolutely not browser agnostic like NPAPI.