Get all comments of author’s posts

It looks like there’s two problem with the code you’re trying to use. The first is AUTHOR_ID. Unless you have this defined somewhere else, then this is going to cause an undefined constant error. The second one is that there should be a closing PHP tag ?> before <?php endwhile; ?>.

Another thing is, that doing WP_Query is a bit unnecessary as you can pass the user ID as a parameter to the WP_Comment_Query directly.

For example on author.php template you could do this,

<?php
$query = new WP_Comment_Query( array(
    'user_id' => get_queried_object_id()
) );

foreach ($query->comments as $comment) {
    echo '<p>' . $comment->comment_content . '</p>';
}
?>

EDIT

To get comments from the author’s posts, use post_author parameter.

<?php
$query = new WP_Comment_Query( array(
    'post_author' => get_queried_object_id()
) );

foreach ($query->comments as $comment) {
    echo '<p>' . $comment->comment_content . '</p>';
}
?>