Stablecoins are tokens issued by a centralized issuer that is backed by fiat and /or US treasuries (especially for USD stablecoins). This would mean USDC by Circle, or USDT by Tether, but there are more stablecoins issued by others as well.

Itch could update the prices pegged to BTC or ETH, yes, but they'd either want to keep them, or liquidate them to USD, in which case there is risk of fluctuation between when the token is sent, and when it's liquidated.