Magento – Magento 2 : Call Static block wysiwyg images not using editor

First off, the code should be

{{block type="core/template" template="custom/employee-links-template.phtml"}}

No need to edit your local.xml you can call your static block in your custom/employee-links-template.phtml template, see below.

   <?php if (Mage::getSingleton('customer/session')->isLoggedIn() && Mage::getSingleton('customer/session')->getCustomerGroupId() == "4") :?>
    <?php echo $this->getLayout()->createBlock("cms/block")->setBlockId("your-static-block-id")->toHtml();?>
   <?php endif;?> 

Explanation: You cannot add children to blocks that are dynamically created with {{block}}, or access them from the layout XML, so you have to create the inner block directly from the template.

You can call theme images from static block like this in magento2 :

<img src="{{view url="images/demo.jpg"}}" alt=""/>