MathType and MACOS beyond Mojave

Ask the vendor.

I'd suspect the code is 32-bit. You can check whether the app is 32-bit yourself in various ways including using Go64, if you have the app installed.

Per the vendor:

1. Will MathType 8 for macOS (macOS Catalina/BigSur) ever be a thing?

Not for the foreseeable future. While we are still considering options, we believe that a math editor embedded as an Add-In or an Add-On is the way to go for the future of our main MathType deployment.

...and...

MathType 7 is compatible with macOS versions up to Mojave 10.14. It is not compatible with 64-bit versions such as macOS Catalina or Big Sur.

Again, ask the vendor.

Asking the vendor may also indicate a level of customer interest to them around more recent macOS support.