Ummmmmmm isn’t that just simple pattern movement? Especially with a simple short song, being able to move it and play it doesn’t help for improvisation. 🤷🏻♂️
I don't think it's simple pattern movement. However, if you learn the intervals between the notes and how those intervals lay out on the keyboard your improvisational skills will most likely improve.
If you take it at face value of "play happy birthday starting on any note at random," sure. It won't help with improvisation. But if you actually zoom out and look at what he's saying holistically? Yeah, it will.
The idea is to help you become able to recreate any melody that’s in your mind, anywhere on the fretboard in real-time. The happy bday song is just an example but it’s not what actually matters here.