Just checked the Kodi add-on and it had the API_PATH variable set to "http://api.giantbomb.com" which no longer works.
Editing the add-on code to use "http://www.giantbomb.com/api" instead fixes it
If anyone feels like doing this, you can open up "C:\Users\<user>\AppData\Roaming\Kodi\addons\plugin.video.giantbomb\default.py" (or the equivalent path on another OS)
and replace the line:
API_PATH = 'http://api.giantbomb.com'
API_PATH = 'http://www.giantbomb.com/api'