It's hard to tell what's actually occurring in that video. But if I had to guess, I'd say that's a Smudge Tool, not liquify. See screenshot. If you don't see it, click the 3 dots icon to customize your toolbar.
Hope that helps.
Nancy O'Shea, Adobe Product User & Community Professional Alt-Web Design & Publishing ~ Web : Print : Graphics : Media
The video mentions Perfect Face and there appear to be apps like FaceTouchUp which are used to visualise the predicted results from plastic surgery. I don't see why you couldn't use Photoshop and the Liquify tool though. The secret to getting good results with that sort of edit is getting the right brush size.
You could also use Free Transform > Warp, but instead of manipulating the control handles, apply the cursor directly to the image. I think I'd want to lift the face from its background if taking that approach, and maybe do the same thing if using Liquify.