What do you call this distorted text effect and how can I reproduce it?

That is just a straightforward use of the Letraset Shatter font (or a clone of it). Shatter is based on Helvetica (obliqued, rotated left, then sliced and displaced if you want to create the effect manually - something that's immeasurably easier with a computer than it was with rub-down lettering and an X-Acto knife); there are similar fonts available (at various prices and quality levels) for quite a few of the better-known display fonts, and in different shatter patterns.