Ahh, yes. The skirmishers of Attila. Can be a lot of fun on the campaign, but they are like a small kid who need constant monitoring.

He he. A few points of importance when it comes to kiting in Attila.
Now about your video. The first thing I noticed was that your cavalry was exhausted. Being exhausted means that your already slow cavalry (75) will be reduced to 65% of it's normal speed. If you are kiting in a forest then an additional 25%. The same can be said for 12 seconds after you were close to slinger's firing range. If you stand in water, then you will be slowed by an additional 50%. As I recall you were exhausted and that in it'self is quite a toll on your skirmishers. In addition to the slowness, a charging cavalry increases it's speed just before it's about to make impact, so keep that in mind you decide to pop Precision Shot.
The stages of fatigue are:
Fresh - 0 no penalties
Active- 1000 -5% to speed - reached after about 11 seconds of running
Winded- 3000 -15% to speed, reload, melee attack - - reached after about 33 seconds of running
Tired- 6000 - 20% to speed, reload, melee attack - reached after about 66 seconds of running
Very Tired- 9000 -30% to speed, reload, melee attack - reached after about 100 seconds of running
Exhausted- 15000 -35% to speed, reload, melee attack - reached after about 165 seconds of running
Every time you position your cavalry close to the enemy, always position them with their rear end towards the enemy. It's not only a great taunt, but it makes the unit better able to run away. The reason for doing this in Attila is the longer turning speed for cavalry in Attila than was the case in Rome 2. Basically, place your cavalry with it's rear end towards the enemy when you manually move them around the map.
I hope that shines some light on the issue. Funny video though, when they don't react like you wanted to.
All that said, there do indeed seem to be bugs with the cavalry's ability to shoot it's arrows. I've noticed some of the cavalry who have 2 precursor arrows never fire their arrows at all.
~Wille