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.

When you run $ mount, you probably see something like this:

ntfs on /media/<username>/Gaming type ntfs (ro,<...>)

If so, that entire filesystem is mounted read-only (hence the "ro" flag). chown (and what you probably wanted, chmod) isn't going to affect that. It alters ownership and permissions on files and directories within a filesystem.

I have no idea what Disks is, but I assume that it's some kind of graphical utility.

I'd probably try doing this, which will only affect the current mount; it won't persistent to the next boot:

# mount -o remount,rw /media/<username>/Gaming

That'll try and remount the thing read-write.

If that resolves the issue, then the issue is going to indeed be that it's mounted read-only.

I suspect that there's probably an option in this Disks thing to mount it read-write. I have never seen the thing, so I can't give any advice there.

If you want to stick it in /etc/fstab and mount it at boot, if you let me see the line you get back from mount above, maybe censoring the username, I can probably tell you what to put there.

EDIT: It looks like the preferred NTFS driver is the FUSE ntfs-3g, not the kernel ntfs or ntfs3. According to the linked page, Debian apparently doesn't build their kernels by default with the ntfs kernel driver anyway, so I assume that Linux Mint Debian Edition probably also does the same. So it'll probably read something like "fuse.ntfs-3g", not "ntfs".