This is what I see in that star.
Each individual diamond section of a Lemoyne star (the red), with strips like a log cabin added just the top two sides of the diamond, for about 6 rounds/fabric changes (I'm guessing 1" strips to finish at 1/2"), final row being a series of HSTs (looks like finished size is 1 or 1.5"), with every other of those rows ending in the red diamond, keeping a sharp and accurate 60º angle.
Then I would think they would take the 8 individual blocks and square them up using a 60º ruler to create a very large diamond, to be sewn to each other, matching seams like you would a Lone Star.
When adding the rounds of strips, I would probably trim the top accurately, but leave the ends hanging out there until I trimmed it up to 60º, because the strips don't go all the way to the bottom.
I hope this makes sense to you. I stared at that star, used a magnifier to view it, and this is what I can make of it.
Maybe if you made just one scrap block to see if it would work out because I'm not at all sure about strip sizes.
Diane