It is common to have time on the x-axis, but that doesn't seem to be the case here. The dots on the line are equally spaced horizontally, but the number of years between each dot varies, sometimes it is 20 years, sometimes it is 40 years, so I don't think the horizontal location represents time.

I'd call this a parametric plot, useful when you have two quantities which vary over time, and you want to visualise how they relate to each other. There are some good examples of that on the Ladder of Abstraction demo, http://worrydream.com/LadderOfAbstraction/ The "Abstracting Over Time" graphic is a parametric plot of the position of the car, where x is horizontal position, y is vertical position, and distance along the line is time.