.
Relevant part is quoted below...
It is an on-chain game and 0.0002 BTC is used in mining fee.
No, it's a "transaction processing fee". Look at Bet #530 or any other bet that lost.

The bet amount is 0.0006
BTC, and the transaction that was given is
981f3689d2ef7e8f477948ea17287eb90472ab189d3c803cb05478b076a3bb64There are 2 outputs - one of 0.0008
BTC, and one of 0.008
BTC. It would seem logical to assume that the 0.0008
BTC was the bet, right? Why would they need to pay the miners fee if the bet lost? Actual 12x payout for this example btw, not the 16x they advertise.
Your assumption that mining fee is not required for a lost bet is incorrect. Let us see how in your example...
First this address was created -
https://blockchain.info/address/1J9uBy5ba1pqtXfYfxzzAxK74qUK1sAfo1User sent the Tx to this address -
https://blockchain.info/tx/981f3689d2ef7e8f477948ea17287eb90472ab189d3c803cb05478b076a3bb64 (User paid the mining fee of 0.000117 BTC)
This address forwarded the fee to the hot wallet -
https://blockchain.info/tx/156a3a82fd231097ea41955f8e5f9c122c055f392179507209ba6404de96f927 (House paid the mining fee of 0.0001 BTC)
So, just to accept a lost bet, house already paid 0.0001 BTC. Now remains another 0.0001 BTC from the Tx processing fee of 0.0002 BTC they mentioned in their FAQ.
Whenever, a winning bet is paid, all these small bets are accumulated and paid from the hot wallet. This increases the Tx size and hence the mining fee required for quick confirmation. So, let us have a look at the latest winning bet right now, i.e. Bet #537.
Wining Tx:
https://blockchain.info/tx/0e6af2f890bac066d349c2b56fff45aa62ddac0fd8b2a5706e5d5212ea5295d9Tx fee: 0.0002 BTC
For this, bet 0.0001 BTC was already with the house from the deposit of the winner of Bet #537. But, who'll pay the rest of 0.0001 BTC? That is taken from the loser of Bet #530. That is how it is compensated.
This is why I said
0.0002 BTC is used in mining fee. I hope it makes sense now.