The speaker treats the whole archive of "old news" as if it were a story about himself. That is the joke of the title: everything in the paper seems to orbit him. But the poem undercuts the swagger almost at once. He admits he knows himself to be superficial, so the self-importance comes with a wink.
The middle lines turn the newspaper into a mirror. His "vanity and liberty" are "drawn in the Times," as though the press had sketched his portrait. His bad years are either "grieved at or pissed upon," a blunt phrase that suggests people either pitied him or mocked him, with little in between. The last couplet lands the sharpest point: any setback is "not fit to print." The record keeps only what flatters, or what is public, and leaves out failure.
The mood is dry, self-mocking, and a little rueful. The speaker seems to see his own ego clearly, yet keeps performing it. The short, clipped lines make the confession feel quick and offhand, like a shrug.