Chrome puts downloads in the Downloads folder under My files unless you've told it otherwise. To choose a folder every time, open Chrome's settings, go to Downloads and turn on Ask where to save each file before downloading.
To keep the clip in the cloud, open the Files app and drag it from Downloads onto Google Drive in the left-hand list. Anything in Downloads exists only on that Chromebook, so moving important videos to Drive also protects them if the device is ever reset.
The new file takes the original's name with "-rotated" added, such as beach-rotated.mp4, so it sits beside the original instead of replacing it.