“steam_osx” is damaged and can’t be opened. You should move it to the Trash.

when you delete the steam.dmg , check the trash for steam_osx exec , run that and it will update the package.

Installing multiple operating systems to your drive many times leads to problems, but it is a way to run the game. Just make sure to always have good verified working backups of your system because modifying partitions and volumes on the drive can lead to an unbootable system or even data loss. Sometimes in order to remove the extra partition requires completely erasing the drive and reinstalling or restoring from a backup.

If you create another partition then you lose a lot of storage capacity (this doesn't happen if you create another APFS volume alongside Catalina). Partitions and volumes are not the same anymore in macOS.

I used to dual boot many years ago, but dual booting is also annoying having to reboot all the time.

Depending on the game and whether your computer supports USB3 you may want to try installing Mojave to an external USB3 drive and running the game externally. It's possible USB3 could be too slow to run the game well, but may be worth a shot since it is less risky than creating another partition.

Try rebooting the computer.

Run Disk Utility First Aid.

Try downloading the Steam app using another web browser.