Why does a screen recording show a black video when I can see it playing?

That can be digital rights management, or DRM. The video provider can require a protected playback path, and the browser, operating system, graphics hardware and video service work together to enforce it. Widevine is one example of a DRM system used for streaming.

The site doesn't necessarily detect your recorder and react to it. Instead, the video can be decrypted and displayed in a protected surface that ordinary screen capture tools aren't allowed to read. The recorder may still capture the rest of the page, leaving a black rectangle where the video was.

DRM is a likely explanation for a paid streaming service, but a black recording alone doesn't prove it. Hardware accelerated video can also be handled differently from the rest of the page, and some capture tools don't grab that video surface correctly.

As a troubleshooting test, try capturing an unprotected video with the same browser and recorder. If that works but the show stays black, protection is a more plausible explanation. Behavior can vary with the browser, operating system and recording tool.

For the credits specifically, try pausing the player or slowing playback if it offers that control. A phone recording of the monitor may also make the text easier to review without relying on a screen capture tool.

Sending the picture to a monitor doesn't necessarily leave it unprotected. HDMI connections can use HDCP, a separate protection system that can prevent an ordinary capture device from recording the signal. Remote desktop apps can also show a blank area for protected video.