I was confused by how CarPlay was working, as this requires the vehicle to be a host and the phone a device, but I'll assume it means wireless CarPlay (vs USB 2.0 CarPlay).
For the display, I wonder if the device is mimicking the assistive touch inputs via external USB PID (per the note) and using a mouse/trackpad HID can take a screenshot via assistive framework - I guess the app could see this arriving, process it and then delete? Also figure out what is being shown? would explain why the video is sped up a little, but YIKES. Also good luck stopping the app being killed in the background.
All direct USB streams require MFI auth, which might work for exactly 100 devices and could be an alternative, but requires Apple cert for bulk quantities.
I think ReplayKit can only work within an app and can't see the general output stream.
Cool use of tech and curious to see how it actually works :)