I'm assuming the shorting is through puts that were bought and held long term, and are being rolled out before expiry? Otherwise a short of the underlying costs money and this has been going on a long time to not close out a position on.
The belief among GME enthusiasts is that the shorting wasn't through puts (options), but rather through straight up short selling.
And that yes, this has been going on a long time and is in fact costing the hedge funds a lot of money. And buying to cover is way too expensive at current market prices, so the hedge funds are bleeding money in hopes that something will change the situation.
Oh, and the belief is also that there are more short sales that need to cover than there are shares of the stock. Hence the squeeze potential.
Closed vs covered are also very different. This hit pieces like to swap them like they're interchangeable too.