The Pythagorean theorem is about orthogonal vectors, so it would just be

  |x + y|^2 = |x|^2 + |y|^2

Plus the line just above that tells you: let

  a = |x|, b = |y|, c = |x-y|

I don't think they are obscuring anything. I think they are showing how the a b and c in the familiar a^2+b^2=c^2 can be generalised to |x|, |y|, |x-y| for any orthogonal vectors x and y in an inner product space.