Maybe some casino gives that warn by popping up the new window and say that they will lose the bonus and the winnings if they want to place a bet over $10. That can help the gamblers know that they can break the rules to deposit or only use a small amount of bet or maybe the casino can send them an email about the warning. The casino can do many ways to give the warning to their members, and I think that will help the gamblers know what they need to do.
That's a good suggestion if those were their own unique games but OP mentioned games coming from third party providers so maybe it's out of their reach to change the limits and if they could change it then the other gamblers playing without the bonus would also get affected by these limits.
This reminds me of the time I had this one bet on esports that ended up winning but the sportsbook decided to void it because of their sportsbook rule where their listed match times didn't line up with the tournament schedule (due to small 5-10min delays), missed out on some winnings but I quickly moved on from that experience.