not all Chromebooks can use Linux, it may just not have it. the android version should work though.
Viewing post in Night Shift at Fazclaire's Nightclub comments
if you just don’t understand Linux right now it is probably best to use the android version as it will be easier to set up and use until you learn what you need to do for Linux. I can’t help with Linux as I have tried Linux myself and also cannot use it, I just use android versions except on this I downloaded it on my desktop
i think this is Unity's fault. it doesn't set the x-bit on the executable, which would tell the system that it's okay to execute the file.
if you haven't already, extract the archive.
most gui file managers have an interface for the read-/write-/executeable bits in the file's properties dialog, which is probably reachable by rightclicking the file. the two i have installed (Thunar & Pcmanfm) have a "Permissions" tab. there should be a checkbox or a some other gui element about execution or execute.
the ultimate solution for any Linux distribution: open the directory in a terminal emulator and run "chmod +x NSaFN*.x86_64". ('*' wildcard so it's valid for future versions.)