I've looked at all 3 of the Real Number videos and the examples just deal with absolute inequality; <, >, absolute equality; =, and what I'll call inclusive inequality and those are the </= and >/=. You'll see these more as you progress further in algebra.
Now, absolute values are just that....they are absolute and always positive...but think of them more as distances from 0 like the instructor said in ex. 2. Additionally, as you progress you'll see absolute values of expressions, polynomials, etc., associated with inequalities. Hope this helps.