This makes no sense to me (and note the target model IS editable once it has been opened, irrespective of the fact that it was accessed via an "open" link), but what the heck, it works.
"Edit" actions (not type) are valid for "file" type links and not much else AFAIK.
EA first checks if the file extension is something it thinks it can make sense of, like .txt or .xml. If so, it opens the file in one of its internal editors.
If the extension is not recognized, I believe the two actions fall through to Windows. In Windows, you can register "open" and "edit" applications per file type. These two do not have to be the same. .xml files are often a good test case; right-click an .xml file in the Windows Explorer and try the Open and Edit menu items -- quite often they will lead to different applications being started (but of course this depends on your Windows configuration).
When EA installs, it registers itself as the "open" application for .eap files -- but not as the "edit" application. (You can verify this by right-clicking an .eap file in the Explorer; there will be an Open but no Edit menu item.)
So if you create a "file" hyperlink in EA and specify the "open" action for an .eap file, when you ask EA to follow the link it tells Windows to "open" the file, which causes another EA instance to be started.
If on the other hand you specify the "edit" action, when EA is asked to follow the link it tells Windows to "edit" the .eap file -- and Windows doesn't know how to do that, so nothing happens.
It would be reasonable to expect EA to say something in this case, such as "no 'edit' action is defined for this file extension". You should file a feature request, or possibly even a bug report.
/Uffe