One anti-piracy measure is to block any screen capture software preventing from anyone recording streams on their PC. However Capture cards exist which intercept the feed from your PC to the monitor and record the footage to a storage device or a PC.
I think the normal way is requesting the stream through a script they made. Normally when you watch a stream stuff is happening in the background that requests the video from the streaming website like netflix. The server thinks the script is a normal user requesting a stream. It bypasses the frontend stuff like what your browser sees and grabs the feed directly from the server and saves it. This is how youtube downloaders essentially work too.
Its more technical then that but thats the eli5 answer.
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