It has the DoraKone.sh batch file and the linux directories under ~/lib so it should work, just run DoraKone.sh. You might have to make it executable first.
Ren'Py games are often ill-packaged for Linux. Especially when they come as .zip archives. Reason is that ZIP doesn't preserve POSIX permissions (like "this file is executable"). Some Linux systems will set the proper permissions automatically for certain file types (like the .sh script) when unpacking, while others sadly will not.
And that's why you were asked to "open that .sh file with a program". Because the executable flag was not set, so it couldn't just run it. With that being the case, the system wouldn't know what to do with the file (Just like when you rename an .exe file under Windows to something else, like .bin. Can't run the program anymore like that, because ".bin" isn't known).
In such cases, you'll have to do this manually. Like this, when sitting in the game folder:
$ chmod u+x ./lib/linux-i686/DoraKone ./lib/linux-linux-x86_64/DoraKone ./DoraKone.sh
That sets the proper permissions on the launcher script and the binaries for both 32-bit as well as 64-bit x86 systems. Afterwards, just launch it like this from your command line terminal, while still sitting in the game folder (or launch it from your file manager by double-clicking):
$ ./DoraKone.sh
I find it strange, that Ren'Py games are often packaged in a way, that requires some slightly more in-depth knowledge about POSIX (UNIX/Linux) systems to make them work there. I mean, if it would be packaged as .tar.gz/.tar.bz/.tar.xz with the permissions preserved properly, such things would never happen...
I assume that is a fault within the Ren'Py development environment itself? Because I've seen this issue a lot. Like really, a LOT.
Should be the same thing, yes. In that case, ToomanyIDs is probably right, and its a file association problem.
If you still feel like pursuing this (I'd be curious), what if you open a terminal window, navigate to where the game is installed (e.g. $ cd "~/Games/DoraKone/" or something), and try to run in from there: $ ./DoraKone.sh. That's essentially also what ToomanyIDs suggested.
Usually, on modern Linux distros, you can find the terminal by just searching for an application named "Terminal". Or browse through your start menu - if you still have one.
If you don't wanna try that (because too much work), it's also fine. :)