Whoops. ~/ is shorthand for your home directory, looks like it would be /home/[username] on Mint. And / is the filesystem root but you seem to have figured it out anyway. I think only the middle step of your fix is necessary for the same effect.
But for the original issue, try doing this: Start MilkyTracker windowed as you would by default. Then in Config > Layout, hit the Custom button next to the Resolutions title. Enter 700 for the width, and 525 for the height, half of your screen resolution dimensions. Then set the Scale to X2 to bump the thing back up to your screen's (I'm assuming) native resolution. Resolution changes do tend to require a restart, so hit OK on the left and do that.
Now, once restarted, it looks like that 700 pixel width is too narrow to actually show the Full screen option next to the Resolutions list but you should be able to toggle full screen with Alt-Enter. Modern OSes, drivers, video cards and monitors are a bit picky about display modes but I have tried these steps on two Windows machines (7 32-bit, AMD mobile GPU / 7 64-bit, nVidia GPU) with 1920x1080 screens and Milky set to 960x540 X2, and it worked for me.