There's a reason Broder is the "doyen." But have you noticed how long Helen Thomas has been around?
Washington tends to reward seniority, including in the press corp, and, after all, when you've made a career out of being a political reporter, where else are you going to go? (Besides State and Defense, a foundation, or a university, I mean.)
FYI, the column was written by "TRB." "TRB" in 1980 was Richard Strout, and had been covering the white house since the Harding Administration(!). He was born in 1898. So, yes, that is an older style of journalism. A few years later, he was replaced by Michael Kinsley.