I just watched it again and I think the "magnified" dots stay the same size as I change distance from the Lite-Brite, but they appear to get larger due to the relative size of the box; the box appears to become smaller as I step away from it, but the dots don't, so the dots look larger in relation to the box. Does that make sense?
Rosette pattern

I think you're spot on - those rosette patterns are known as moire when it comes to video. Cool effect with that new-fangled Lite-Brite.
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