It was not apparent from your article how Timsort ensures stability. After doing some reading on my own I was able to discover that it is done so by only reversing strictly decreasing runs, and by never reordering runs.

While your description covers both of those points[1], it didn't mention them together as contributing to stability.

1: Actually rereading to make sure I didn't miss anything, you have a mistake, as you say: "Runs have to be strictly increasing or decreasing" while they have to be either monotonically increasing (i.e. non-decreasing) or strictly decreasing.

so: 1,2,2,3 is a run, but 3,2,2,1 is not.