Google has little incentive to support H.264 when they have their own, competing WebM format that they are trying to push. (Haven’t you ever wondered why such a relatively unknown format is one of the formats the YouTube, a Google subsidiary, supports natively?)
Unfortunately, as you have learned, they re-structured Chromium so that you cannot easily drop in H.264 support as you could before. In fact, they have been planning on dropping support for H.264 altogether (even from Chrome) for a couple of years. They plan on switching completely to the WebM by providing WebM plugins for other browsers. (Hopefully they will continue to support JPG and PNG despite trying to push their WebP format.)
What you can try instead, is to use the Microsoft plugin that lets Chromium play H.264 through Windows Media Player. Because it is a plugin, it should still work—unless Google specifically blocked it.