Counting the number of post without custom post type

One way to do it would be to run two custom queries like this:

$normal_post_args = array(
  'post_type' => 'post',
  'category_name' => 'hobby'
);
$normal_posts_query = new WP_Query( $normal_post_args );

$movie_post_args = array(
  'post_type' => 'movie',
  'category_name' => 'hobby'
);
$movie_posts_query = new WP_Query( $movie_post_args );


echo "Posts (" . $normal_posts_query->found_posts . ")";
echo "Movies (" . $movie_posts_query->found_posts . ")";

This should give you something like Posts (5) and Movies (3). That’s a starting place. Then it’s just a matter of wrapping this in a function and referencing it in your template file.

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Update:
Based on your comments, the best way I can think of to do this would be to create your own category list, rather than using the default WP one.

Something like this:

$categories = get_terms( 'category');
if($categories):
  echo "<ul>";

  foreach($categories as $cat):

    $cat_posts = get_posts('post_type=movie&category=' . $cat->term_id . '&numberposts=-1'); 
    if($cat_posts):
      echo "<li>" . $cat->name;
      $count = count($cat_posts); 
      echo " ($count)"; 
      echo "</li>";
    endif;

  endforeach;

  echo "</ul>";
endif;