Not sure that tree is the oldest living thing. According
to this site, there are a few contender for the title. But regardless, it still must be something to see something that old, still alive.
As you point out, there are other contenders. There are various creosote rings, including one about a mile from my house, that are thought to be in excess of 11,000 years old. A couple of years ago I read about ancient pines, IIRC, somewhere near the treezone in Norway, which tested older than the Bristlecones. However, these pines and creosotes are clonal plants, and I don't think the Bristlecones are.
FWIW - I've seen both old creosote rings and old bristlecones, and the bristlecones have my vote as the more impressive plant.