If you want to play them out the HDMI and recapture them in Final Cut you will need a way to capture them. FCPx does not really deal with capturing real time video files, or at least the way other programs do.
Most Capture cards come with capture utilities that will do this. You then import the files into FCP.
Can you get to the files as data files and transcode them? It would save you the costs of capture card.