How to get if child category of this category is empty?

You’re going to need to loop over the $re_child_terms array. According the docs get_term_children returns an array of term_ids so you will need to loop over the ids, get the terms and save them into a new array if they’re not empty.

$re_child_term_ids = get_term_children( $term->term_id, 'category' );
$re_child_terms = array();

foreach ( $re_child_terms_ids as $child_id ) {
    $child = get_term($child_id);
    if ( is_object($child) && !($child instanceof WP_Error) ) {
        if ( $child->count > 0 ) {
            $re_child_terms[] = $child;
        }
    }
}

if ( $term->count > 0 || !empty($re_child_terms) ) {
    // do stuff
}

// note: this code is untested but should work

EDIT (encapsulated into a function):

// in functions.php
if ( ! function_exists ) {
    function get_nonempty_term_children( $term_id, $taxonomy ) {
        $child_ids = get_term_children( $term_id, $taxonomy );
        $child_objs = array();

        foreach ($child_ids as $id) {
            $child = get_term($id);
            if ( is_object($child) && !($child instanceof WP_Error) ) {
                if ( $child->count > 0 ) {
                    $child_objs[] = $child;
                }
            }
         }

         return $child_objs;
     }
}

// in template
$re_child_terms = get_nonempty_term_children($term->term_id, 'category');

if ( $term->count > 0 || !empty($re_child_terms) ) {
    // do stuff
}