[Kranar]

Someone who is just learning chess will likely be able to beat the old them with 99% probability after a few days of playing and learning.

Someone who is ranked at around 1200 and really commits to improving can likely beat the old them in a couple of months by memorizing a few common openings and practicing drills/working on fundamentals.

Someone who is a dedicated chess player and ranked above 1800 may never be able to beat the old them with 99% probability.

So if someone says they improved by 600 points, certainly that is meaningful to them as an individual and it means they can basically beat their old self, but it won't be very meaningful to me.