Its not an array, its an object(-tree).
echo $obj->results->{"http://www.domain.com"}->shortUrl;
Should work.
Also it looks like you are receiving this structure as JSON I guess? Then you may use the second parameter of json_decode()
to make an associative array out of it.
$array = json_decode($json, true);
echo $array['results']['http://www.domain.com']['shortUrl'];
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