Nice, Channels DVR supports ARM

Download the setup.sh file, and it looks like ARM is supported.

I doubt it would run very well on the Pi Zero. It would probably run fine on the RockPro64. Assuming you don’t need to transcode anything. You need an Intel CPU for hardware transcoding.

HDHomeRun network TV tuner
1GHz CPU (64-bit Intel, or 32-bit/64-bit ARM)
512MB RAM
Large HDD for storing recordings
HDTV is on average ~8GB per hour

According to that, it has enough RAM, and I think it’s at least 1 GHz.