I'm guessing you have not installed the codecs for the default Windows app to play MKVs. That doesn't mean a problem with the file.
Where an OBS recording is saved is configurable by you. You are responsible to make sure there is enough throughput (bandwidth) to write to that disk target (an potential problem on a laptop to record externally via USB, and also using a USB webcam... you can overwhelm maybe the USB Root Hub controller)
So, you have 2 choices... look up how you can setup Windows to play MKV videos, or remux the MKV to MP4 file so your existing software can use it. One is not better than the other. Microsoft chose to enable WAV, MP4 and certain formats/wrapper/encoding streams, and not others by default. VLC player is a common freeware tool to add support for other formats.