You are totally right (except W, which doesn't Really matter )
It was mainly just AP-HP item for maximizing ult DMG, since it gives you 400HP = +40 dmg and 65 AP = +32.5 DMG so +72.5 dmg in total.

But it was just what I intended to build in the video, I didn't yet have time to finish the thoughts behind the build, I think one would benefit more from Rabadon's Deathcap perhaps, but still, we have few other things which benefit from additional HP like Grasp of the Undying Overgrowth, Heartsteel and Riftmaker.


Here is an example of my thought process:
If we get another 400 hp - It will scale with Overgrowth giving us more max HP as well.
It will also give us more AP trough Riftmaker making it more than just 65 AP.
But also each time you now proc your Heartsteel, it gives you more max HP than it would otherwise, starting the cycle of HP scaling once again ...


That's why sometimes it is Hard to decide since we would have to count if the HP scaling doesn't give us more damage in the long run.