Magento 2 Widget – Only Shows One Way Issue

I've created a Catalog Products Lists widget to use my own template when the items are displayed on the frontend. When I insert the widget via Content > Widgets > 'Add Widget' and set it to be displayed on a specific page (CMS Home Page) and in the Main Content Area – everything works fine… The products are displayed as I'd like them to be.

Now, if I try to add the same widget via Content > Blocks > 'Add New Block' > 'Insert Widget', the following is added to the CMS Block content:

{{widget type="Mike\ProductList\Block\Catalog\Product\ProductList" title="Widget from CMS Block" category_id="26" template="product/list/productlist.phtml"}}

Unfortunately, my widget isn't being displayed in the CMS Block I created. Any ideas why the widget is displaying fine when added via the Widgets page and not being displayed when added to a CMS Block?

UPDATE:
In response to Aaron Allen's suggestion

My current etc/widget.xml file looks like the below:

<?xml version="1.0" encoding="UTF-8"?>
<widgets xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:module:Magento_Widget:etc/widget_file.xsd">
<widget 
    id="category_product_list"
    class="Mike\ProductList\Block\Catalog\Product\ProductList"
    is_email_compatible="false"
    placeholder_image="Magento_Widget::placeholder.gif" >
    <label translate="true">Catalog Product List</label>
    <description translate="true">Displays a list of products in a block using my new template</description>
    <parameters>
        <parameter name="title" xsi:type="text" required="true" visible="true">
            <label translate="true">Title (frontend)</label>
        </parameter>
        <parameter name="category_id" xsi:type="block" visible="true" required="true">
            <label translate="true">Category</label>
            <block class="Mike\ProductList\Block\Adminhtml\Catalog\Category\Widget\Chooser">
                <data>
                    <item name="button" xsi:type="array">
                        <item name="open" xsi:type="string">Select Category...</item>
                    </item>
                </data>
            </block>
        </parameter>          
        <parameter name="template" xsi:type="select" required="true" visible="true">
            <label translate="true">Template</label>
            <options>
                <option name="default" value="product/list/mikeProductList.phtml" selected="true">
                    <label translate="true">Product  Template</label>
                </option>
            </options>
        </parameter>
    </parameters>      
</widget>

As you can see, this is telling my widget to use Mike\ProductList\Block\Catalog\Product\ProductList as my class.

<?php

namespace Mike\ProductList\Block\Catalog\Product;

use Magento\Catalog\Block\Product\ListProduct;

class ProductList extends ListProduct {

}

How would I tell the widget to extend Template and implement BlockInterface, if I'm already extending Magento\Catalog\Block\Product\ListProduct to pull in the products?

Do I need to create another class (the one you posted) Magento\Widget\Block\BlockInterface and tell the widget somewhere in the XML to use that too somehow?