> Why wouldn't they double down?
Because short sellers accept potentially unlimited liability in the event of a price increase. Remember the old maxim: the markets can remain irrational longer than you can remain solvent.
The operating theory of the WallStreetBet hivemind is that the short sellers (collectively) are in so deep that further price increases will force them to close out their positions by buying back stock at a loss. Short sales are ultimately made on margin (because they're a debt of a share), and margin accounts will be called in at some ratio.
That "short squeeze" would cause the price to spiral ever further, and that price increase would then force any remaining short sellers out of the market.
See https://moxreports.com/vw-infinity-squeeze/ for a well-known, circa 2008 short squeeze that happened to Volkswagen.
The issue with the operating theory is that it's fuzzy; there's no way to know what price point will trigger such a short squeeze.
> I don't buy individual stocks and even I'm tempted to get in on the short side right now. Seems like an easy way to turn $1k into $10k.
Only if you are highly leveraged yourself, exposing you to those dramatic losses if you mis-time the market even slightly. If you do want to take the down-side of Gamestop, it'd be safer to buy a put option to limit your potential loss. However, the high implied volatility also makes the trade a bit expensive right now.
(Edit to add: I have no financial interest in Gamestop, up or down.)