I think you can try the following options.
wp_list_categories with the 'show_count' parameter
http://codex.wordpress.org/Template_Tags/wp_list_categories
get category and use $count = $category->category_count;
http://codex.wordpress.org/Function_Reference/get_category
You can traverse up the functions to get_term if those don’t work and see what is in there, even though you probably can use get the terms you will have to parse the array for output as can be seen in your example, so the above 2 methods would most likely be better.
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