How do I block specific websites?

I wish there was a viable workaround, but the simple answer is "no" unfortunately.

What's triggering the browser invocation is a system-level intent, and basically any app is allowed to open web browsers using the default protocols from anywhere, similarly to being able to e.g. trigger a phone call request, open the app store, or invoke a calendar.

Your default browser gets launched to the foreground by the operating system, and only after waking up it's passed the target links etc. — so even if there was some extra filtering on the browser side, it would always end up opening anyway, as it's just being invoked by the iOS at that point without knowing anything about the kind of content or the opener game :(

Firefox Focus doesn't really provide a normal blacklist where you can enter specific websites and block them. Its built-in protection is mainly aimed at trackers and other unwanted content. If the game is opening those sites in Firefox or another browser, look at blocking the ad domains rather than trying to block the pages themselves. On regular Firefox, an extension such as Block Site can block specific domains and URLs. If the ads are opening a completely separate browser window, though, blocking the domains may not always stop the app from launching the browser. In that case, the better solution may be to block the offending domains at the device or network level.