The battery is dead.
It's also possible the charge-level sensor is out of calibration, but unlikely. To calibrate it wait until it shuts off on its own and then charge it fully with the PHONE OFF.
But if it happens again, and it probably will, the battery is toast.
What's going on is that there is a low-voltage safety cut-off for Lithium chemistry cells. The reason it's present is that over-discharge can result in an internal short in the battery, which will then cause the cell to overheat and explode when charged. There is a protocol to get around this risk (essentially you charge it at a VERY LOW current level until the voltage comes up; this detects the short if it exists and avoids the problem) but you don't want to short the cell as that ruins it permanently.
As cells age they cannot deliver current at the required level without the voltage collapsing. If the voltage collapses then the phone detects that as a low-voltage cutoff violation and shuts down. If it happens materially before the power level is at 0% (fully discharged) then the cell is junk. It may appear to charge and work ok but if you actually measure its capacity using an accurate means (I have a bench charger/discharging unit that can do so) you'll find it's pretty-materially deficient in its capacity.
The reason Accubattery (and others) recommend only charging to 80% is partly because fully-charging Lithium chemistry cells does do more cycle damage than not (and there's no "memory effect" to avoid with them) but also because cellphone manufacturers intentionally over-drive the charge rate to shorten charge times. The correct means to charge a Lithium chemistry cell requires 3 or 4 hours, and nobody wants to wait that long. You can get into the 60-80% range very rapidly (with careful calibration of the charge controller you can run your charge rate at 1C, which would mean at 3,000ma for this battery) but once you reach 4.2V you hold voltage constant until current drops to about 3% of rated capacity in ma/h (so in this case that would be about 100ma.)
The problem with doing this is that the saturation charge cycle is a couple of hours. Total charge time doesn't change much but the higher the rate you run the bulk charge at the lower the actual capacity when the threshold voltage is reached, so if you were to charge at 3,000ma you'd probably see threshold at 60-65% instead of 80% if you ran the charge at 1,500ma.
Manufacturers however want to sell you "fast charge time!" so they run their bulk phase up higher, in some cases in excess of 4.3V. Beyond 4.3V there is risk, in that plating of lithium can happen and if it does you can get plating of metallic lithium, gas production in the cell (which makes it bulge) and ultimately the potential for thermal runaway and fire. The cells are supposed to have both a temperature and pressure switch in them that permanently disconnects the output if this happens (but as we've seen with certain phones and laptops that doesn't always work.) The other issue, however, is that stuffing the charge rate like this stresses the battery severely and shortens its service life -- it will take what was a 500-cycle battery and turn it into a 200-cycle one.
The only defense against that -- and the manufacturer's decision to screw battery life in favor of "fast charging" -- since you can't reprogram the charge controller is to disconnect it at 80% or so and do not "float charge" (e.g. leave the phone plugged in overnight) at all.
BTW there are some manufacturers of laptops (specifically, Lenovo in their X220) that come with their chargers set to NOT do this (they only charge to 95% and use a proper taper with NO float charge, so it really does take 3 hours or so to fully charge their batteries!) and the difference in service life is very, very material. I have one of these and have had to replace the battery exactly once in seven years of ownership; the replacement is still well within manufacturing tolerance (about 90% of original capacity.)