I know this was months ago, but in case anyone else has this issue, do either of these things to install an .sh on GNU/Linux:
Open terminal in the directory/folder wherein is your Stardew Valley installer.
Type: chmod a+x [name of installer].sh
Then hit "enter"
Type: ./[name of installer].sh
OR
Type: bash [name of installer].sh
Then hit "enter"
In either case, after you type the first commands, you can also type the first couple of letters of the installer and then hit "Tab" and it should autofill.
Let me know if there are any issues.