If you notice in the picture below, you can have the students watch the video on one side, and then type their notes on the other side. Each new line they begin typing will cause the timestamp to appear in yellow. If you want to go back to a specific note from the video, you can click on the note, and it will take you back into the place where it appears in the video.
If you notice in the top right in the picture, you'll see that all changes are also automatically saved in drive. You can also export them to evernote if you wanted. You can have the students share their notes with you so that you can keep track of if they are taking notes or not in the class.
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