If you provide the value for datadog_api_key in ansible vault and try to run using the call back it will error with a message much like this:
PLAY [localhost] ***********************************************************************************************************************************************************
Could not load configuration, invalid file: [some path]/plugins/callback/datadog_callback.yml
This is because on line 237 the api_key and url are loaded from the .yml file. If the file does not exist then it errors. Later on line 240 there is code to load the value from ansible vault.