So, I approach issues differently to Randy. Instead of 'jumping to cause', I try to understand what you actually did instead of making assumptions on what you did:
When you say you've enabled it, did you do the following:
Enable it?
Then create an API key as directed?
Was it approved by GIPHY?
Did you then enter it in the ACP, and save it?
Because only then would you get the icon in the editor that provides the integration (which, by the way, is theme independent as it is a CKEditor plugin):
Did you then use that button to search for your chosen GIF?
Or did you manually paste in the URL for the GIF?