From the deficient test suite you can see an example of how it's intended to be instantiated (I've obscured an email address and the API key, but you can find them in the test file):

# API Key provided by ____@im__r.com
my $apikey = "b3625162_____________805b1840452";
my $imgur = new Image::Imgur(key=>$apikey);
ok( $imgur );
my $result = $imgur->upload('http://st.pimg.net/tucs/img/cpan_banner.p
+ng');
ok( $result );
[download]

There is this explanation in the docs for WWW::Imgur:

Image::Imgur is an alternative module for imgur.com. It uses the XML version of the API rather than the JSON one which WWW::Imgur uses, and it depends on the Moose module. It uses an older version of the Imgur API.

I noticed also that WWW::Imgur says that even that module (WWW::Imgur) is using the deprecated API, so the one that Image::Imgur is using must really be outdated (and possibly no longer operational).