Can I use an emailed Apple Gift Card to pay an online casino?

I kind of doubt it, more from the perspective of the casino. They would have to have an Apple account and be willing to accept that the money would only be used to purchase other items from Apple. They could not turn it into cash.

After that, it is up to the casino. If you send the the code they could redeem it.

You don't say how you are using this Casino. If there is an app for the casino (I never do things with casinos so I have no idea if they are even allowed to have apps) then you might be able to use one. I get the impression, though, that for something like that a casino might want a more guaranteed method of payment such as a credit card.

The other indirect method would be if the casino literally purchased to gift code from you at a greatly reduced price. Of course this would then be more work for them if they then were re-selling code to somebody who actually wanted to buy something from Apple.