Found the Problem. I didn't think about it before, but the file separator for Windows is "\" and for Linux it is "/". I had that problem in another project before so i'm a bit mad at myself for not noticing. The Proper way of doing it is
Path.GetFullPath(Application.dataPath + Path.DirectorySeparatorChar + filename);
Path.DirectorySeparatorChar replaces the "/" or "\".
I tested it and it works for Linux. Since it changes the char according to the Operating System it should work for Windows and Mac as well.
I created a file named ThatGame_Data\platformsettings.txt in the Folder which contains the ThatGame_Data Folder and was able to finish the Level that way xD