The PS3 is one such media player. It supports the codec (x264), but not the container (.mkv). One solution to this is the program "mkv2vob", which leaves the source audio/video untouched and just transfers it to a new container, such as .mpg. Because it leaves the source content untouched, processing a 1.2 GB file only takes a few seconds and there is no loss in picture or audio quality. You can find mkv2vob here: http://www.mkv2vob.com/
Documentation for ReadyDLNA does seem to be either very lacking, or very well hidden, one of the two.
Note however that different equipment may support more than this. eg ReadyDLNA supports streaming .mkv, so I guess in your case it is the client that doesn't support .mkv