As per amazon's documentation (https://docs.aws.amazon.com/apigateway/latest/developerguide/api-gateway-setup-api-key-with-console.html) I am supposed to see a dropdown near API KEY. Although I have admin access I don't get such an option.
Please assist setting up authorization in API gateway using API Key.
From your screenshot it looks like you are setting up Mock integration - that doesn't support authorization. You can only enable API KEY in real integration, not in Mock.
Hope that helps :)