Here's the answer:
Right now, its still running because the water is overflowing the top of the overflow riser. Normally, I would tell you just to lower the level at which the fill valve shuts off, because the water isn't getting high enough relative to the fill valve to fully-shut-off the fill valve.
However, it looks to me like the fill valve float is fully-submerged and has pressed the shutoff off. But the thing is still running.
So, after trying the above, which probably won't work (i.e. lower the shutoff point for the fill valve), there are two possibilities. One is that the valve is defective. The other is that your water pressure is so high that it is pushing past the fill valve even through it's trying to shut off the water.
Both are unusual, but I would first try just replacing the fill valve (and get the Korky 528MP ("Platinum"); it's just easier for homeowners to install properly).
I would also buy a cheap water-pressure valve that you can screw on to like a hose bib and check the pressure. If it's much above 75, you've got a higher-than-normal pressure. But that valve should probably hold back pressure to 85 or more, so if it's a pressure issue, you're gonna get a very high reading. Most people are comfortable with 60psi on the low side to 75 on the upper side. 80 is about as high as you'd want to see.
A little valve like this
http://www.homedepot.com/p/3-4-in-Plastic-Water-Pressure-Test-Gauge-DP-IWTG/100175467?cm_mmc=Shopping|THD|G|0|G-BASE-PLA-D26P-Plumbing|&gclid=CKyv7PmknM4CFcIkhgodQFUIHw&gclsrc=aw.ds is something you can screw on and leave for 24 hours or more; the one hand tells you what it is now, the other hand tells you how high it has gone. Sometimes, it's normal during the day and goes way up overnight when nobody is releasing the pressure, etc.
To review: (1) adjust the 400A lower and see if it shuts off about 1/2" below the top of the overflow riser; (2) replace the 400A, maybe with a 528MP that you have adjusted so the line on the valve is 1/2" below the top of the overflow riser, and see if it shuts off at the right place; (3) if 1 and 2 don't work, then check your water pressure, which is likely way too high.
EDIT: Looking carefully at your video, the water is already WAAAAY over the top of the float, which it shouldn't be. The float on the 400A usually lets the water almost overflow it, then pops up and shuts off the water. The top of it should never be submerged in normal operation.
One possibility, and it's hard to see from your video, is that you have installed it so that it is rubbing against the side of the tank and can't pop up all the way. Make sure that it can float freely. You would just need to loosen the nut below (with an empty tank) a smidge, then spin the thing a little bit clockwise to clear the side of the tank, then tighten the nut; if that's the issue. If it's not, then step (1) is probably already moot, but I would check to make sure the float is moving freely.
Frankly, from your recitation of the original symptoms before you did anything, I'm guessing water pressure, but let's do the cheap and easy steps first. If you want to post a video of the flush and refill, that might help, too, but I think we've given you everything you need.
