Installed a steam game through one user but no write permissions from other?

I downloaded CS:GO steam in Linux Mint Tricia 19.3 through a standard user (spectra) and an administrator (darkguy) (tried both ways). Installed directoty :/mnt/227ad523-2b06-456b-908f-fbda67a95046/Steam Library
Currently it is installed through spectra (group-spectra), and most of the files are owned by spectra, so darkguy has no write access on them. (Even though darkguy has read access and steam can find already installed game files).
Is it supposed to be like this?
How do I correct this? (Individually changing the files is beyond impossible). Just migrated from Windows.