You can create a Canvas assignment for a video quiz that you created through My Media. You will need to do this if you would like it to be added to the gradebook.
Create a new assignment in your canvas course
Add a warning in the description for your students to complete the video quiz in one sitting If they need to come back to the quiz later, they should refresh the page and start from the beginning.
Now add the amount of points the quiz is worth
Under Submission Type click external tool
Click Find and scroll down and select Kaltura Video Quiz
Locate the appropriate video quiz from the list and click Embed
Click Select when you are brought back to the Configure External Tool window
Add a due date and availability information as necessary