It's rare that spinning floppies ruin drives completly.
Unless the little sliding hatch has bent or become unshaped and pulled on the heads, it's more likely the disk squeels on the inside jackets. These jackets are there to remove small dust particles etc but with time also can become flat and have a greater surface area to the plastic floppy biscuit. The squeeling is probably just slowing down disk rotation and therefore you are getting mis-reads.
A good claen of your drives heads carefully with a cotton bud and tape head cleaner (same used in VCR or cassette) should work, or use a floppy disk cleaner.
The game may also be ok. If you are very careful, buy new disks, pop open the case and exchange the biscuits. Wourst case is heads are dirty. Miss alignment from reading the disks is very unlikely.
Hope this helps.
I have successfully transplanted many biscuits (inner round disk) into new jackets and read them successfully.
Good luck.
