SSMS 2014 does not launch Graphical Execution Plan from clicking hyper-linked query plan - ShowPlanXML
You need to ensure the System Registry contains the correct file-extension-mapping for .sqlplan files.

Open the Registry Editor, navigate to the following key:

Computer\HKEY_CLASSES_ROOT\.SQLPlan


Confirm the (Default) value contains something like:

ssms.SQLPlan.14.0


(the version number might be different for SSMS 2014).

This is a screenshot of Registry Editor showing the key and value:



You'll also need to ensure the following value is set correctly:



When I say "correctly", I mean appropriately for your system.  If this approach doesn't work, I'd try simply re-installing SSMS 2014.  Of course, I'd actually recommend installing the latest version of SSMS, v18, which is available for free directly from Microsoft.