The special thing about ITC is you can do the splitting (to add a member) and joining (to remove one) without any external coordination. They otherwise are used in the same way as vector clocks. I find the linked post more confusing than I remember the original paper being (I wrote an implementation):
Hmm yeah, I think I glossed over that point when reading the article.
Looking at the paper you linked, I think the clock can be generalized to operate in Q^n. In other words, it doesn’t need to be a real valued space, and it doesn’t need to be bound by to special case of 1 dimension (interval). It only needs to arbitrarily subdividable and have the appropriate boundaries.
http://hydra.azilian.net/Papers/Interval%20Tree%20Clocks.pdf