Planes aren't spherical and don't change directions in all ways as easily... so taking the straight line distance isn't as helpful as you'd think.

You can't really compare horizontal and vertical distances.

This is correct, and it is implicitly recognized in the vertical separation intervals being less than the horizontal ones. What matters even more than distance, however, is time, and in this case, fortunately, the aircraft were travelling in the same direction and so had a low closing speed (it was actually negative, I believe.)

Presumably they plugged it into the Pythagorean theorem.