Here's a style plugin validator function that checks for the presence of specific fields.
To specify which fields are need, add a key to the style plugin definition of the form:

  'required_fields' => array('field_machine_name_1', 'field_machine_name_2'),

/**
 * Validate a view for specific fields.
 * Add a key to the style plugin definition of the form:
 *  'required_fields' => array('field_machine_name_1', 'field_machine_name_2'),
 */
function views_plugin_validate_required_fields($type, $view, $form) {
  $plugins = _views_get_style_plugins();
  $plugin_id = $type == 'page' ? $view['page_type'] : $view['block_type'];
   
  if (is_array($plugins[$plugin_id]['required_fields'])) {
    // build a list of fieldnames
    $id = 0;
    while (is_array($view['field'][$id]) ) {
      $fieldnames[$view['field'][$id]['field']] = TRUE;
      $id++;
    }
    foreach ($plugins[$plugin_id]['required_fields'] as $required_field) {

      dsm($fieldnames);
      if (!$fieldnames[$required_field]) {
        form_error($form["$type-info"][$type . '_type'], 
          t('The @style style requires the field @field.', array(
            '@style' => $plugins[$plugin_id]['name'],
            '@field' => $required_field,
          )
        ));
      }
    }
  }
}

Possible improvements: this gives the machine name in the error message. It would be better to get the field's human-readable name out of views data so the user has a better clue of what they need to find in the field drop-down to fix the problem.