WordPress can build the menu two ways. The normal way is that it assigns pages to the menu based on the hierarchy you assign in the Page Attributes section. The Parent and Order determine where the page will show on the menu. This is probably what’s going on with Website #1.
The second way is to build a custom menu. After you build the custom menu using the Menu section you need to assign it to a menu area that your theme provides. If you forgot that step, or your theme doesn’t allow custom menus then it won’t show up. In your video, for Website #2 I didn’t see any area to assign the menu for your theme. Check with your theme developer to see if it supports a custom menu.