So I accidentally opened an mkv video file with Chrome, and to my surprise it played it using the native player:
<video src="video.mkv"></video>
It was playing perfectly. HTML5 video supports matroska container?
HTML5 doesn't support any video formats, or rather HTML5 doesn't specify what formats browsers should support. It's up to the browsers to decide which formats they choose to support. Apparently Chrome plays .mkv, but I wouldn't be surprised if other browsers didn't play the same file.