Creating a wordpress video header on home page only

@Owen, There are several ways to do it.

First: You can do it from Backend.

Create a page "home" and add the video from Media button and Choose this page as "Home" from Setting -> Reading --> Static Page

Second: You can create a home page template and put the video Url path in that page manually and display it.

the best way I suggest you use the plugin called "fullpagejs" in that you can create a video slide with auto-played video and map that slide to your home page. this should work very fine.