EME doesn't "allow" proprietary code, that's a misinformation of Wikipedia based on this four years old post , a post which does not provide real information, just the assumption that at some point a full DRM solution will be integrated into the browser.
The EME is just an API to interact with the license server and the Content Decryption Module. This CDM is the one responsible for decrypting the video. It runs in a sandboxed environment, so no access to your computer is needed.
The whole purpose of EME is to not need a plugin to use a DRM system, so you don't need to rely on third party plugins (Flash, Silverlight...). Therefore, you are removing an often vulnerable point.
In summary, the EME doesn't add any security at all from the server side, but it provides security in the client side removing the need of installing a third-party plugin.