You've got it right. I was going to label the inputs in the transistors in the second animation, but it made the diagram rather crowded, so I left it out.

The diagrams are simplified because they leave out things like connections to ground, attached resistors that mitigate the total current, etc. But I wanted to convey, as simply as possible, how transistors worked and how gates could be made very simply out of a small number of transistors.

The actual CMOS chips in use by ARM (and still in use today) complicate things more, because you have different types of silicon (NMOS and PMOS) on the same substrate, so the transistors work slightly differently and you can simplify making things like NAND gates, which themselves can be combined to make all other types of gates. For this article, I didn't want to get that deep into the woods, though. :)