Our long-term strategy is to make it so that nobody needs to use plugins by adding new web APIs
The illustration on the page you linked uses Silverlight as an example. Netflix uses Silverlight so that it can wrap rented videos in Microsoft's PlayReady digital restrictions management, and lack of PlayReady is why it doesn't work in Moonlight. Video on demand providers use digital restrictions management in the first place to deter users from in effect teeing a rented video into an encoder and keeping it past the rental period. How would VOD work on a browser distributed as free software without any proprietary plug-ins?
The page you linked states: "As browsers have advanced, this kind of feature development can occur directly within the browser using technologies such as WebGL" but this page, on Firefox 25.0.1 on Xubuntu 12.04 LTS on a laptop with an Atom N450, states: "Hmm. While your browser seems to support WebGL, it is disabled or unavailable. If possible, please ensure that you are running the latest drivers for your video card." A lot of users aren't in the position to buy a brand new PC just to be able to switch from Flash or native apps to web applications.
The page also mentions asm.js, but do non-Firefox web browsers, such as Chrome, Safari, and IE, support it yet? Otherwise, will have to write the program several times: once in asm.js for Firefox, once in Native Client for Chrome for PC, once as a native app for Android if the user hasn't already switched from Android Browser or Chrome to Firefox for Android, and then once as a native app for each platform that IE or Safari runs on.
and to use the mobile web as leverage to get new sites to use native HTML APIs
That won't especially help when Apple refuses to implement key HTML APIs in its iVersion of the mobile web. True, Safari for iOS can't run Flash anyway, but the idea on mobile is to get developers away from making platform-specific apps.
Quick question: Using HTML APIs, how should a web application let the user select a folder (or "directory" if you insist) on the local machine and upload all files in the folder?