올려주신 코드를 아래 코드로 교체해서 적용해보시겠어요?

add_action('kboard_pre_document_update', 'kboard_pre_document_update_210816', 10, 3);
function kboard_pre_document_update_210816($content_uid, $board_id, $content){
	global $wpdb;
	$user_email = get_userdata($content->row->member_uid)->user_email;
	$pre_category1 = $wpdb->get_var("SELECT `category1` FROM {$wpdb->prefix}kboard_board_content WHERE `uid` = '{$content_uid}' ");
	$category1 = $content->row->category1;
	$document = new KBContent();
	$document->initWithUID($content_uid);

	if($board_id = '1' && $pre_category1 != $category1){ // 게시판 id
		if(!class_exists('KBMail')){
			include_once KBOARD_DIR_PATH . '/class/KBMail.class.php';
		}
		$url = new KBUrl();
		$mail = new KBMail();
		$mail->to = array(get_option('admin_email'), $user_email);
		$mail->title = "카테고리 변경";
		$mail->content = $content->content;
		$mail->url = $url->getDocumentRedirect($document->uid);
		$mail->url_name = '페이지로 이동';
		$mail->send();
	}
}

$board_id 에는 실제 적용할 게시판 id를 작성해주세요

고맙습니다.