And although OBS is most well known for being incredible streaming software, the fact that it can handle smooth video recording from games too (since once you have streaming you can pretty easily have recording too) means it's also displaced other video recording software such as Fraps, which used to be the go-to tool when recording games.

Wirecast has existed since at least 2008, with most of the same core compositing and switching functionality we see in the space, although originally Wirecast did not support RTMP. It was originally only able to stream to QuickTime RTSP servers and Windows Media Server.

XSplit emerged slightly before OBS Classic but OBS innovated with a far superior game capture implementation on Windows, supporting shared texture hooking across D3D8-D3D11 and OpenGL, which helped it gain massive traction with the Twitch crowd. After retaining a large user base it was eventually rewritten as the cross-platform OBS Studio.

For quick recordings, the screen recorder built into the Xbox Game Bar (Win+G) also does the job.

Why Microsoft decided to put this functionality only in the Game Bar (and not also in, say, the Snipping Tool) is anyone's guess...