How to make a vote in the poll for registered users?

You can check user logged in with is_user_logged_in. This is a simple function to check user logged in or not. Can you try this?

<ol class="zf-structure-list zf-quiz_answer zf-text zf-clearfix">
    <?php
  if(is_user_logged_in()){
    if( isset( $question["answers"] ) ) {
        foreach ($question["answers"] as $answer) {
            ?>
            <li class="zf-answer-item <?php if (isset($_COOKIE["zf_poll_vote_ans_" . $answer["answer_id"]])) echo 'zf-selected'; ?>"
                data-voted="<?php echo isset($poll_results["answers"][$answer["answer_id"]]) ? $poll_results["answers"][$answer["answer_id"]] : 0 ?>"
                data-id="<?php echo $answer["answer_id"]; ?>" data-post-id="<?php the_ID() ?>"
                data-group-id="<?php echo $question["question_id"]; ?>"
                data-voted-group="<?php echo isset($zombify_poll_results["groups"][$question["question_id"]]) ? $zombify_poll_results["groups"][$question["question_id"]] : 0 ?>">
               <div class="zf-answer js-zf-answer">
                   <div class="zf-checkbox-wrp"></div>
                   <div class="zf-poll-stat"></div>
                   <div class="zf-poll-stat_count"></div>
                   <div class="zf-answer_text">
                       <?php echo $answer["answer_text"]; ?>
                   </div>
               </div>
            </li>
        <?php
        }
     }
} else {
 echo 'Please login to show these poll';
}?>
</ol>```