Disclaimer: I am very new to Linux (1 week).
I have installed the Valve version of Steam on LMDE6. I have used Disks to automatically mount the NTFS drive I used with Windows (doesn’t hold bootloader, it is just for Steam library storage) at boot ( /media/[username]/Gaming ) and I made it the default library folder in Steam.
Running games works perfectly (actually, performance is surprisingly good), but I cannot install them due to a “disk write error”.
I looked for solutions and found this page, from which I understand that I need to change permissions to the mounting point, but when I do, using chown -R, I get a “Read-only filesystem” error for all files and folders.
I can see no options to fix this in Disks and I tried to edit fstab once, but it messed things up so badly I had to use the USB drive with the portable installer to fix things.
Like many others here, I think the most likely explanation here is that you did not fully shut down Windows and it still holds a lock on this partition. You can force an actual shutdown in Windows by shift-clicking on the start button -> shutdown.
However, I would also recommend against sharing your Steam library between Linux and Windows. I also tried this with NTFS a few years ago and it caused me a lot of headaches. I had a lot of weird issues under Linux that went away after I finally switched to ext4.