It doesn't have to be linked to age, just a yearly probability summed over more years.
Then you can start adding in the things that make people live longer, like less heart disease per year of life, etc., and you get the same effect they are charting.
If the effect isn't related to age, then what you're describing is captured by population.
Any cancer is related to age in the sense that the older a person is, the more opportunity they've had to encounter it. I suppose the best way to look at it is see how many cumulative years a population represents: if a population is getting older on average, then the cumulative years have risen, therefore there's been more opportunity to encounter this disease.