Update: They don't have trees between 40kya and more recent ones. So this tree just happens to straddle the period of interest, and to provide carbon samples from each year, in labeled sequence; but without exact registration to specific years you can get from trees less than (exactly!) 12,311 years back.
There are other ways to get annual carbon samples, e.g. peat bogs, but they are subject to various kinds of corruption, such as roots, and disturbance, so it's harder to establish the ironclad evidence you get easily from tree rings.
Dating events by tree reings is called dendrochronology. The priciple use for this tree's evidence is dendroclimatology, and maybe dendrogeomagnetology.
Also, you can check the carbon ratio in a particular ring. That gives you a sample of the air from that year. Because, you know, trees are very, very literally made out of air.