I gather from your question that you are looking to automate this process, correct? Or are you just thinking of something that will allow you to easily standardize each image so that the subject looks the same size through out the series? Looking at that video, you can see the author used several tricks to ensure equal sizing throughout the series and at a level of detail that I suspect were all done by hand.
I have used LR to equally crop multiple photos at once by using the "Previous" function so that every image gets the same treatment (tone, crop, size, etc.) as the original standard image. You would then need to go back by hand and re-position each image to get the eyes centered at the proper place but your image sizing would all be the same. However, it would require a lot of image by image work.