The MPEG2 headers are messed up, this happens more often than you'd expect.
As I understand it, on a DVD, there are 2 places that store the aspect ratio. The first is in the MPEG2 header (the actual video file) and the second is in the IFO's (which so far as I understand is like a description of what's in the video).
Anyway, when you rip to an MKV, it's only concerned with what's in the MPEG2 data stream, and thus if the DVD has been mastered incorrectly you get squashed video. DVD players it seem pay more attention to the IFO file than the MPEG2 header, which seems like the wrong way to do things, but that's just how it is.
Anyway, the issue is fixable, but you'll have to do the following:
1. Extract the video stream from the MKV file with mkvextract (part of the
mkvtoolnix package).
2. Open the raw video file with DVD Patcher (
download here).
3. Edit the aspect ratio to be 16:9, tell it to patch the whole file, make sure the other settings are also correct (resolution etc...)
4. Open MKVmergeGUI (part of the
mkvtoolnix package) and add the MKV file you started out with, but untick the video stream and move it to the bottom, then add the patched video stream from step 3 and move it to the top so it's the first stream.
5. Mux the whole file back together and you're done.
Yes, it's a pain, but there's not much to be done about it. With these 5 steps you know for sure that your video file is 100% correct and will play on anything.