Will you come to that point that you are going to ask for KYC?
I might depends on location where MintDice placed their company, and license they have (if they have it). Most of online casinos don't ask for KYCs, but there are some exceptions, especially if someone withdraw huge money, KYCs are required, just in those cases.
High amoint of money really needs KYC but if you are player who withdrawing small amount of money KYC will not need for sure. But I don't think Mintdice will required KYc because player did not want KYC and as a team they did not allow to decrease their player because they requiring KYC.
This is a common misconception and its not true. It doesn't matter whether its large amounts of BTC or small amounts, as long as your deposit is not from shady sources then most gambling sites won't have issues giving you a withdraw or ask for KYC.
There are only a few sites that require KYC and one of them is that Pornhub casino and they require KYC because they accept credit card deposits. And there are 1 or 2 shady gambling sites that force KYC when you got a big win and they don't want to pay out so they use KYC as a last resort because they know that many people might forfeit the winnings, its only shady casinos that do this.
Some large casinos might have KYC in the past and that was only because the deposit was from a tainted address, basically it was some stolen BTC and it was sent to the casino and didn't make any bets and a withdraw was attempted, so they tried to use the casino as a mixing service and got their funds frozen.