This wouldn't be possible unless something was constantly polling the API to see what's playing. It's doable, but not great. For automations like this to work well, you'd need the device to publish something when something happens, and the Channels API doesn't do that.
You can run a small cronjob on the server running the DVR to regularly query the DVR about its status, and then take action if it meets a certain criteria. (Or a better route may be to query the device in the room where your "Movie Night" scene is, and when it detects that a certain show is playing, then it will send the signal to set the HomeKit scene.
(Although, I think you'd need something like HomeBridge or similar to make this work ...)
You could create a "The Walking Dead is Playing" sensor. Then have it get set to on/off when the show is being watched. Then you could create automations off of that. When on, do movie time.
You'd need something like a REST or HTTP sensor that could poll a URL and interpret the response in a way to let you set the state of the sensor to ON or OFF.
I've been out of the Homebridge game for a while so I'm not sure if it has that. But Home Assistant has the restFul Sensor. You just give it a URL and tell it how to read the JSON response to produce a state for the sensor.
They're pretty powerful.