The error message means your browser considers the yEd installer a plain text file and tries to open the installer in a text editor (gedit). That will not work. After accepting the license terms and clicking the "Download yEd" button, your browser should either automatically download the file to your hard disk (e.g. Chrome does that on my system) or ask what it should do with the file (e.g. Firefox does that on my system).
(If Firefox does not ask, you probably downloaded another *.sh file and checked the "Do this automatically for files like this from now on." In that case, go to "Edit" -> "Preferences", tab "Applications", search in the "Content Type" list for "SH file" and reset the associated action to either "Always ask" or "Save File".)