My Nexus 6p is the same. At exactly 15% battery if I open specific apps I immediately get notified that my battery is 0% and my phone turns off. This only started within the last 6 or so months.
The voltage written on a standard battery cell is the "average" voltage the cell will produce across its life time.
As amperage is spent(?), the voltage will drop slightly, so the cell will start out higher than listed and end lower than listed.
What is likely happening is that the when a certain app is started, various parts of the hardware is clocked up to handle the work load. This result in a higher draw, and a sharp drop in the measured voltage, in turn the power management logic considers the battery nearly drained and shut down.
Never mind that unlike older battery chemistry, lithium batteries do not take kindly to being fully drained. Thus there will be a programmed safety margin involved.