Sadly, nothing kept the protein. It's fossilized, just like everything else with the bird. The proteins are identified by their placement in the cells. The scientist mention they could be other microbes that they were fortunate enough to have the colors left for better context.
Carbon dating is not a magic bullet and would not work here. C14 dating can't be used to date samples more than 50,000 years ago because C14 has a relatively short half life and most of it would have decayed by then(0). Additionally, C14 dating doesn't work on fossils because much of the carbon has been replaced by different minerals.
Uranium lead dating is typically held as accurate for rocks between 1 million and 4.5 billion years ago, so they probably used this. However, there may not be any uranium in the fossil itself so they may have looked at stratigraphic layers of volcanic ash, which would have sufficient amounts of uranium, above or below the fossil to arrive at this date(1). This is really speculation without looking at the study where I'm sure they discuss it in detail.
Funny, when I read this, I thought it was about a bird whose feathers were essentially unchanged for 130 million of years of existence - it didn't occur to me until I saw the article that it was about fossilization.
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