The example at the start of Section 13.2 describes marathon runners and runners not finishing the race as a possible example of right censoring. This seems like a bad example to me.

I would classify the event where a runner doesn't finish the race as a competing risk (an alternative event preventing the primary event from occurring), rather than right censoring. Right censoring should refer to cases where the observation period ends before the event occurs, but the event itself still happens later. (Exactly as it is explained in math afterwards).

For example, an instance of right censoring in this scenario would be if we stopped observing runners after a fixed time limit, say 3 hours, regardless of whether they finished or not.