Add HTML5 required attribute to webform fields set as required
You will need to create a module for this. 
Note that, this answer assumes you need to set required attribute on all form elements which are required in web form settings. 
you will need to implement a different hook and/or add conditions to make this strict. 

Create a file named webform_formalters.info and put following to it. 

name = webform form alters
description = a collection of custom form alters for webforms. 
core = 7.x
package = Custom
dependencies[] = webform


Create another file named 'webform_formalters.module' and put following in it. 

&lt;?php
/* 
 * implements hook_form_BASE_FORM_ID_alter. 
 */
function webform_formalters_form_webform_client_form_alter(&amp;$form){
  //dsm($form);
  foreach ($form['submitted'] as &amp;$field){
   if (is_array($field) &amp;&amp; isset($field[#required]) &amp;&amp; $field['#required'] == 1){
     //dsm($field);
     $field['#attributes']['required'] = 'required';
   }
  }
}


Put both files to a folder named webform_formalters and upload to your site's module folder and enable the module. See if it works. 

Unlike other forms, web forms' fields are stored in $form['submitted'] array. So we go through each item (which should be an array of form definitions) and check if the element has marked as required. 
if so, we add or merge required attribute. We are altering an existing form, so we are not going to pop out existing attributes.

Good luck!