My Big Fish games will not play on Catalina 64-bit

Refer to this excerpt from Big Fish Games Help:

Updated information for macOS Catalina!

With the release of macOS Catalina (10.15), Apple has made the decision to stop support for 32-bit apps. This means that systems running macOS Catalina (10.15) and newer will not be able to play our 32-bit games. 

Check out our instructions about how to download and play select games 64-bit apps on macOS Catalina! 

To learn more about macOS Catalina, please read our help article.

I agree. Why not check with the game provider and see if a 64 bit version is available?

Probably because they are 32bit games.