The article clearly identifies the source of this exceptionally well-preserved fossil (NOT soft tissue) as Hamilton Quarry in Kansas.
Hamilton Quarry is a well-known site of many well-preserved fossils from the Carboniferous era.
World-wide Carboniferous deposits are dated from around 360 million years ago to about 300 million years ago, and account for much of the world's coal supplies.
How is geological dating accomplished?
The gold-standard is radiometric dating, for which there are dozens of different materials that can be used, depending on a stratum's age.
For just two examples: carbon-14 is very accurate back to around 60,000 years ago, while Uranium-lead is accurate within around +-2 million years, but all the way back to billions of years ago.
Uranium-lead samples also come with built-in cross-checks using both U-235 and U-238.
Are all of these methods fool-proof?
No, of course not, they all have to be double-checked, cross-checked and re-checked to be sure the answers are consistent with everything else known about the samples.
But given that many thousands of such tests have been performed, over many decades and all over the globe, the consistencies of results are about as good as you can ever get in natural-science, and support every other theory we have (i.e., evolution) about the natural history of ancient Earth.
Yet dating systems other the carbon dating require many absurd assumptions that are impossible to falsify thus making them scholastic authority not the scientific method.
“There are but two ways of forming an opinion in science. One is the scientific method, the other, the scholastic. One can judge from experiment, or one can blindly accept authority. To the scientific mind, experimental proof is all-important, and theory is merely a convenience in description, to be junked when it no longer fits. To the academic mind, authority is everything, and facts are to be junked when they do not fit theory laid down by authority”
From the short story “Lifeline” by Heinlein who was one of the first to speak out against the “settled science” of academia, way back in the 1940s.