It could be either. Is the pain sharp during motion, or is it a dull, sore type of pain? The first is bad, the second is good/bad.
I injured my lower back and noticed a few things after it happened. First was that it was the sore type of pain and thus I used ice for 48 hours and heat after. Since you're passed 48 hours, use heat on the back.
Second, I'm not sure what motions are in this video which could cause lower back pain. Most injuries do occur when the muscles are overloaded or strained - they are tired and siphon off the tension and the strain moves to tendons, ligaments, bones, and other nearby muscles. That's when something gets pulled, so yes, your lower back was probably in a weakened state, "gave out" and shifted its responsibilities elsewhere.
Take time off - the lower back is super important. As for strenghtening it, moves should always be performed, in any exercise, with what we call a "braced core". This is when you breathe in before the strenuous part of the motion and kind of hold the abs, obliques, and back in a structured, tight manner while performing the move. If not, then the move isn't done correctly and the strain, again, finds it way to weaker places.
Then you are healed up and only then, try buddha squats - fold your arms across the other, feet shoulder width apart, and do full body squats. After a while, you should notice that your lower back is getting a great workout. You don't need weights in your hands or on your back to do these kinds of squats to help strenghten the lower back. And each should be performed with the braced core.