Probably this is a dumb question, but there are some videos captured from FPV Freerider. I wonder how those videos were captured.

Open Broadcaster Software is one example of a software you could use to record and even stream your desktop (and applications).

OBS - https://obsproject.com/

There are many other around, like FRAPS for Windows, Camtasia for Mac, SimpleScreenRecorder for Linux and so on...