Okay, this is a first.
I don’t have a linux OS to have tested this before, but the Renpy engine automatically builds distributions that should work on Linux.
Inside the folder you downloaded you’ll see a file named nif.sh. Try to double click it and see if it runs. If not…
You need to mark the nif.sh file as executable.
(Note: if you don’t know how to do it: This may be slightly different depending on your Linux distribution, desktop environment and language. Right-click the file, select Properties -> Permissions -> mark as executable)
Then go to the "lib" directory and open the adequate Linux directory (linux-i686 or linux-x86_64) and look for a file named nif (without any extention). Mark this file as executable too.
(Note: If you don't know which Linux directory is right for you, do the same thing for the nif file inside both of the directories)
Try double clicking again in the nif.sh file.
Did it work?
If not, try to run in through the terminal. I have found here a 10 min youtube tutorial explaining how to do it with another renpy game (it also shows and explains all of the steps above). Just try to do the same steps for this game that has a nif.sh executable.
I hope this helped.
If you still can’t make it to work, I’m afraid I can’t help more than this. Sorry.