Batteries actually lose very little voltage over a discharge cycle right up until the point of complete failure.
As the charge is dissapated the internal resistance of the cell increases and consequently prevents the cell from giving full calculated (at full charge) circuit current. In laymans terms the current runs out long before the voltage does.
The X axis shows the cell characteristics normalised as a percentage of cell capacity so that the shape of the graph can be shown independent of the actual cell capacity. If the X axis was based on discharge time, the length of each discharge curve would be proportional to the nominal capacity of the cell with the lithium ion curve in particular disappearing off the end of your monitor.
I like him ... He says "Okie Dokie!"