If I understand correctly, the drivers for a bunch of tuner cards are in the mainline kernel:
https://www.kernel.org/doc/html/late...vers/ivtv.html (also firmware link for Conexant chipset)
You don't need anything fancy to grab the /dev/video0 stream: mplayer/mencoder, ffmpeg, xine, etc even just 'cat /dev/video0 > my.mpg" As mention above, the encoders for capture for these old cards are just ghastly. You might what to check the Card list and see if you can pick up a cheap newer version.
Come to think of it, I should try my old Leadtek WinFast 2000 card to see if it still works (assuming there is even an analog TV broadcast here). The old 2.6 kernel and drivers where gimpy back when and Its not like I'll ever fire up Windows 2000 ever again.