There are people who like to write, there are people who need to write because of their work, and then there are people who are “writative.” The difference is probably something like this: someone who likes to write might keep a journal, but having forgotten to pack their diary for a weekend trip, would simply skip it until they returned. Someone who needs to write for work is perfectly able to write, but typically writes only about job-related topics. But someone who is writative might try to skip their journal entry for a day, but would end up writing a several-page entry about the effort. They would write about job-related topics, and also about the experience of writing about job-related topics, and the possibilities enshrined in all those attractive non-job-related topics.
Someone who is writative is simply addicted to writing. That sense of writative postdates the way Alexander Pope used it in his 1736 letter to Jonathan Swift, which said:
“I Find, tho’ I have leſs experience than you, the truth of what you told me ſome time ago, that increaſe of years makes men more talkative but leſs writative: to that degree, that I now write no letters but of plain buſineſs, or plain how-d’ye’s, to thoſe few I am forced to correſpond with, either out of neceſſity, or love: And I grow Laconic even beyond Laconiciſme; for ſometimes I return only Yes, or No, to queſtionary or petitionary Epiſtles of half a yard long.”
Somewhere between 1736 and the early 20th century, when “writative” pretty much disappeared from usage, the word acquired its addictive connotation. Pope clearly means the milder “inclined to write.”.
Pope, by the way, is pretty inconsistent in his application of the “long s” — the ſ character. Even though it comes from the days when spelling was more a set of general inclinations than rules, I think when he writes “neceſſity” he would have been better served by “necessity” (doubling the “s” letterform gives you a long “s” identical to the “ſ”). But in the years since 1736 writers of English — whether writative or not — quite sensibly asked “why do we have two different letterforms for “s”? And even more sensibly, the answer was “um…no particular reason; let’s just pick one or the other.”