So I accidentally opened an mkv video file with Chrome, and to my surprise it played it using the native player:
The website has probably set the mimetype of the file to video/webm. Chrome will open this inline rather than forcing a download (because otherwise it doesnt know what to do with it or how to open it).
E.g., in apache this is done by using the AddType directive (can be done in a htaccess):
AddType video/webm .mkv