Get in the box, Barbie- or we'll make Ken do it again.
If anyone's wondering why this works so well, both Barbie Girl and Cruel Angel's Thesis use a circle progression in their intro/chorus, and since the songs are only a half step apart (Barbie Girl starts in C# minor, Cruel Angel's Thesis in C minor) shifting Barbie Girl down to fit Cruel Angel's Thesis is fairly subtle and doesn't sound obviously manipulated.
I only recently started taking music theory/analysis seriously (after having been a no-theory knowing mfer even after decades of playing instruments) and it has been incredibly rewarding! I've got a long way to go (my goal is to be able to play songs by ear without needing to sit down and do analysis or trial-and-error), but it's been so exciting to start seeing how songs are put together and finding similarities between songs that I never realized were there.