Earlier quoted context omitted.
If anything it's the opposite. Defining a standard interface for content decryption allows such a system to be browser agnostic. You install a module and it works in any browser which implements the spec, whether proprietary or open source.
Unless they've changed it since I looked, the only interface the HTML5 EME specification defines is the one between the website and the browser. There is no standardized interface between browsers and DRM modules, nor is there any requirement browsers support external content decryption modules. For example, last I heard IE was only going to support a built-in implementation of Microsoft's PlayReady which isn't avail…
It looks like the idea is to implement a system where encrypted content is passed to the browser. The key is then sent through the browser to the CDM, the CDM can take the content and hand back decrypted frames.
It's entirely possible for content vendors to support multiple CDMs for different browser or OS combinations. The advantage of this is that the CDM is a smaller dependency than something like silverlight, so you can have a standard HTML5 video player interface across platforms and just swap out CDMs.