If investors get their account balance reduced because of house losses, is it stated what kind of game (dice or slot) caused this house loss?
No. The only reason I was able to find this out is because the bet showed up on the public big wins table.
When I click your link, it shows only the recent rolls for the past minutes. Do you have any other source for his win?

You can see these stats live by going to big wins and clicking last 30 days.
Based on what do Satoshi Slot share the same bankroll as Satoshi Dice?
1) Knowing my investor balance before and after that day.
2) Seeing this win of 303 BTC that correlated to the amount of site bankroll lost.
If you have something to add, please leave a reply below the article.
I can inform that take Satoshi Slot losses out of the investor account is 100% sure a scam, as it is nowhere mentioned in the "Bet on the house" terms and conditions that investors are part of Satoshi Slot's bankroll.