We have build-in functionality to make extra galleries for each product variation and as you can see you are allowed to select images http://prntscr.com/1ys0sp9 but not allowed to select videos for variations. Accordion to your products we see that you have predefined variations and our code works in the next way:
1/ Single product page is loading
2/ Once it is loaded, WooCommerce trigger action that makes a request that tells there is predefined variation (in simple words it is like you clicked on variations just when page became loaded)
3/ After that our product variations script starts to load data of variation that is triggered (clicked)
4/ It gets data and replaces the default content of the slider with product variation’s one.
So that’s why you don’t have product video after page is fully loaded.
We would recommend you to disable predefined variations to make your default gallery with videos loads on start and only when user will try to change options (colors/sizes/etc.), it will replace your gallery with gallery of product variation.
