Output checkbox per user and save in plugin options

Change the [user] to [users][]. Hope that will fix the problem. Now you’ll get all the value in associative array within [users]['your-checkbox-data-array'] So your code will be like-

<?php
   $WPusers = get_users( 'orderby=nicename&role=administrator' );
     foreach ( $WPusers as $user ) { ?>
       <input type="checkbox" name="<?php echo $this->plugin_name; ?>[users][]" id="<?php echo $this->plugin_name; ?>-users" value="<?php echo $user->ID; ?>" <?php checked( $user->ID, $options['users'], false ); ?> />
       <label for="<?php echo $this->plugin_name; ?>[users<?php echo $user->ID; ?>]"><?php echo $user->display_name; ?></label>
     <?php } ?>