The first meaning is, effectively, government by bureaucrats. The first part of the second meaning is probably extendable to all forms of news media, given it was coined when the only form around was newspapers. The second part of the second, I assume is wishful thinking. The OED claims this is a nonce-word, created for the occasion, but if so it's been independently created several times, enough to look like it's alive in the wild, so to speak. Coined from Greek roots papyros, paper or papyrus + kratia, power, strength, along the lines of democracy, theocracy, kleptocracy, and so on.*
I'd like to adopt, but there's so many approvals -- you have to prove you can parent to a papyrocracy.