The fact you're confusing option types is not helping your credibility. Writing put options is a bullish move. Melvin may have been writing CALL options (I doubt it to be honest but maybe).
Melvin had $55 million worth of put options on GameStop, which are the opposite of calls. Puts assume the share price of a stock will go down and give their owners the option to sell a stock at a certain price. Melvin assumed GameStop’s stock would fall, and bought puts allowing Melvin to sell GameStop’s stocks above the market price, netting Melvin a profit.
Melvin is that it was also shorting GameStop, meaning it was borrowing shares of GameStop, selling them on the market and using those proceeds to make other investments. Problem is, Melvin eventually has to return those GameStop shares. So now Melvin has to buy GameStop at their new, inflated price, only to give those shares back to the original owner