If bitcoin goes up a lot, would the fees also go up?
If the dollar value of bitcoin goes up, the fees (in terms of satoshis) wouldn't increase. They would either stay the same or the devs would decrease the minimum withdrawal requirements and you would spend less sats. The only difference is that those sats are now worth more than what they were in the past.
Your mistake is thinking in dollar amounts and converting the values to $. If the withdrawal fee of a casino is 0.0002 BTC and bitcoin goes up by 50%, but the fee still remains 0.0002 BTC, the fee hasn't increased. It has stayed the same. It's up to the casino operators to even out the changes.
Most of us are not mature enough to think in bitcoin terms only. Whatever the withdrawal fee is, we normally first convert it in dollars and if the bitcoin price is higher, we think that the withdrawal fee is too much.