So NTFS doesn’t support Linux-style ownership. fuse should be able to mount it read-write using usermode drivers.
Do you have write access at all? Can you create a text file on the drive? Sounds to me like your problem isn’t just Steam-specific, but rather that for some reason it’s defaulted to a read only mount for some reason - maybe a change to the fuse driver or the kernel ntfs support.
I don’t have any NTFS-formatted drives to test with, unfortunately… all of the computers in our house are Linux or Mac, so for drives that only touch Linux we use ext4, and drives that are used by both it’s either nfs or exfat. :( How big is the Steam library, and do you have a decent Internet connection? Save games are usually in your user folder, regardless of where the library’s installed, so if it wouldn’t mean an enormous & time consuming download it might actually be worth reformatting the drive using a Linux filesystem.