To be brutally honest, that's not riding a shortboard, that's just standing up and being pushed along by the whitewater on a shortboard
That wave barely looks worth surfing, let alone on a shortboard. There's no steep section and no power. The unridden peak above you might have just about had a beach close-out worth riding for a nanosecond, but it's out of shot when it breaks (if it does). Between the peaks (if we're being charitable) is a flat section so you haven't got anywhere to go... but you don't even try and just get your tail stuck in the whitewater.
Right, to be more constructive... (which is a bit hard, there isn't much to work with)...
Your paddling speed look likes it's improved, but I think you're slowing yourself down by sinking the tail - move just a couple of inches forward, which will mean arching your back more to keep the nose out of the water.
Make sure you've lifted your feet out the water - the wave should catch the board, not you.
The board is horizontal and straight towards the beach as you pop up - shortboards should be facing down and along the wave (but you haven't got enough wave to pop up with).
You pop up into a standing position then crouch back down again - your pop up should be straight into the crouch position without an intermediate step. Practise this one at home!
If I'd been on the wave (and I do take scrappy little waves on my shortboard, just for fun, quite regularly)...
I'd have been so far over the front of my board that the nose was sinking. My right foot (I'm natural) would have been raised above my bum to bring the weight even further forward.
I'd have paddled at a slight angle (the wave hasn't got enough power for a proper angle) and I'd've dropped my weight over the front of the board until I was damn sure I'd caught it.
Then, in a split second, pop up! Weight on front foot to drive! Leading hand right out in front of me! Weight onto the inside rail, weight partially onto the back foot! Look up and along the line! To the top of the line, still driving! Leading with my hand and my shoulders, weight back onto the inside rail and down the "face"! If possible, repeat!
(Actually I'd've spun out over the top of the wave after the first bottom turn because that's what I like to do on small waves, but lets stick to basics for now...)
In all honesty, I'd say that a shortboard was a poor choice for that day. And, if you want to shortboard, as someone said to me the other day "you won't get better if you don't go bigger".
