The "HTML5" support requires proprietary binary blob that has no standard API (besides an API to launch it with opaque data from a proprietary server) and is licensed only to selected companies.
Basically it's as much HTML5 as <object data="swf"> was HTML4.
It's supported only by DRM vendors: Google (WideVine), Safari (FairPlay) and Microsoft (PlayReady) and doesn't work in open-source browsers (not even in Chromium or custom WebKit builds).
You can't make a web browser that plays Netflix without signing contract with one of the DRM vendors that Netflix supports, or rolling your own DRM and convincing Netflix (and distributors that pull their strings) to adopt it.
For example if you compile Chromium from source it won't work (at best Netflix will send you encrypted blobs that you won't know how to decrypt and there is no public spec for it anywhere).
From video publisher's perspective it's locked-up as well. To have your own video DRM-protected with the same tech as Netflix you'd have to get a license from Google (for Chrome WideVine DRM support), Apple (for Safari FairPlay) and Microsoft (for IE PlayReady DRM).
Netflix's playback without "without plugins" is achieved not by removing plugins and having open standards, but merely by convincing browser vendors to bundle closed DRM code with their browsers. Technically it's more like Chrome shipping bundled Flash, but fortunately nobody calls that a "HTML5 native Flash without plugins!"
Where do you cut the line? It's a plugin because it uses the plugin api? And were it integrated in the main binary, would you call it a "plugin-less proprietary HTML extension"? I think the main differentiation point is that it's made by the browser authors, shipped with the browser, updated with the browser. That, to me, means that it's not a "plugin", even though it uses the plugin interface; it's an implementation detail.
"Plug-in" in the web browser context also had a wider meaning of "3rd party proprietary binary blob, that has limited portability, and adds functionality and APIs that are not part of Web standards."
You're right, technically EME's integration and distribution are different, so it's not a plug-in in that sense. However, the other downsides that were associated with plug-ins have remained the same in the built-in ex-plugins.
Browser plug-ins get so much hate not only because they're pain to install/upgrade, but also because they're usually not as open and portable as the rest of the platform.