It looks like you won't be waiting for Windows 10 to pick up native support for MKV files in Windows. An update for Xbox Video on Windows 8.1 rolled out tonight that brings support for the video format, along with several fixes.
MKV support on Windows 8.1 is the latest example of what seems to be a relatively recent embrace of the format by Microsoft. Back in October, we saw a Windows 10 Preview build pick up MKV support, along with the Xbox One shortly before that.
While MKV support is the most notable change here, you can find the full change log below:
Support for MKV videos (the extension used for the Matroska Media Container). The update supports playback of most MKV files as long as they contain streams that use codecs supported by the app. For more information on MKV support on Windows, please check out the related article about support for MKV on Xbox One. The implementation is the same on both platforms except that V_MPEG2 is only supported on the console.
A fix that makes our Spotlight section more robust
A fix for an issue that caused the Rent button to appear when viewing TV series and shows
A fix for an issue that was causing file metadata to appear in the video title in your collection
Fixes for two issues in deeplinking to content within Xbox Video from other apps (the movie details page and playing trailers, specifically)
Feel free to hit up the link below to get your MKV on. Also, let us know how it works out for you in the comments below.
Source: Xbox Video User Voice