Loop counter style

You can use the Modulo Operator in PHP to check if the loop count is odd or even and then assign those elements a CSS class based on that.

$class="listpostsright";
if ($wp_query->current_post % 2 == 0) {
    $class="listpostsleft";
}

Things to note:

• In programming counting begins at 0, so this logic may look a bit
  backwards, but it should work.

• You don’t need to a variable to count the loop WordPress has already
  provided that in the $wp_query object.

• And never use query_posts use pre_get_posts instead.

Update:
Here is an example of how to use this in your template.

<?php
// Use pre_get_posts to alter your query.
// This would be done in your functions.php
while (have_posts()) :
    the_post();

    $class="listpostsright";
    if ($wp_query->current_post % 2 == 0) {
        $class="listpostsleft";
    }
?>

    <article id="post-<?php the_ID(); ?>" <?php post_class($class); ?>>
        Positioning of your elements here, you should be able to do with css alone. Unless it is much more complex than your example.
    </article>

<?php endwhile; ?>

Arithmetic OperatorsPHP

pre_get_posts