The gamma squeeze also works going down, if they had to load shares on the way up they have to unload on the way down, accentuating a down trend.
When you drive the price of the stock up you increase the interests the short have to pay on the shares they borrowed to sell, or maybe increase the capital requirements they need to maintain this position on their books, reducing their upside.
If the interests or the capital requirements for maintaining the position get too high, or the owners of the shares want them back, they might have to exit their position, "no matter the cost" hence the "squeeze" part.
(I'm writing it down to see if I understood it all correctly)
When you drive the price of the stock up you increase the interests the short have to pay on the shares they borrowed to sell, or maybe increase the capital requirements they need to maintain this position on their books, reducing their upside.
If the interests or the capital requirements for maintaining the position get too high, or the owners of the shares want them back, they might have to exit their position, "no matter the cost" hence the "squeeze" part.
(I'm writing it down to see if I understood it all correctly)