The guide I linked explains the tools of OBS that can do what you want to achieve.
1 start with a fresh scene setup
2. set Settings->Video->Base resolution to your monitor resolution
3. add a display capture source and make it so that you see this source in the preview (usually standard). Click on the source, you will see the borders and small red circles at the edges of the source.
4. crop your desired area by holding ALT down and move the small red circles with the mouse, so you cut out your small video clip
5. drag the cropped source to the top left corner of the preview
6. open Settings->Video and as base and output resolution enter your desired resolution that should contain the video file or stream. You will enter a much smaller resolution now, to minimize the black area around the source. Ideally, you set it exactly to the size of your cropped source.
7. right-click your source and in the popup menu select Transform->Fit to screen to make the source the size of your new base resolution
voila, you have your small video cut out from the display and made it the only component of your output video.
However, it can be much easier, depending on the type of the app that displays your small video clip. There are numerous source types you can add instead of display capture. If your video is generated by some app, try a window capture source and add this app directly. If your video is generated by some game, try a game capture source. If your video is generated by some media source (video file) or stream, add a media source or VLC video source.