Welcome to Linux and Ubuntu is the best choice.
Installing programs on Ubuntu is extremely simple. But there's one main difference of Linux with Windows.
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On MS Windows, file extensions determine the file type. *.exe is an executable, *.txt is a text file.
On Linux, the file type is determined "inside the" file and can be altered. This ensures maximum security and is one of the main reasons why Linux is far more secure than Windows.
So on Linux, you can create a file, and name it my_file.txt. Open it with a text editor, write some code, then make that file an executable and run it.
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Now back to your situation. The files you downloaded are not automatically executable. If you trust the source, the easiest way to make it executable is:
"right click the file >> properties >> Permissions >> Check "Allow executing file as program"
That's it. Now you can double-click it and it will run as intended.
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Linux thrives on "packages", a group of shared codes that makes the systems run. And as systems improve, some packages are "dropped" in favor of others. And since most GOG installers assume (or expect) some packages to be available by the system, some old wraps may not always work.
In order to see what the problem is, the best way is to run the package in the terminal, so you can see what you are missing. Let's say that your game installer is called Game.deb (It can also be game.ls. The procedure is the same)
1. Go to the folder Game.deb is in. Do this the "windows" way, normally, without the terminal.
2. Now right-click anywhere inside that folder and select "Open in Terminal". The terminal will open in that folder
3. type
ls
This will list the files and folders inside where you are. Make sure that Game.deb is one of them.
4. type
./Game.deb
Note that if you just type ./G and then press TAB to autofill. Press enter.
TRAP!! Linux is case sensitive. So if the file is Game.deb, and you type ./g and press TAB, it won't auto fill. Also, it won't run if you type ./game.deb or ./GAME.DEB .
I love trolling my windows user friends by sending them 5 different files named like (game, Game, gAme, GAME etc), and then they can see all 5 files but can't open them unless they can solve the puzzle. A fun mental exercise.
5. This will try to run the file and output any errors with missing dependencies along the way.
ENJOY!