Wordpress - How to get template drop down menu in page-attributes of custom post type?

Well, as of Wordpress 4.7 custom templates are also available to custom post types, when defining a template, below the name of the template add another line like (where 'product' is your custom post type):

<?php
/*
Template Name: My custom layout
Template Post Type: post, page, product
*/

// your code here

and remember to add 'page-attributes' when registering your custom post type:

'supports' => array('title', 'page-attributes'),

to display the "Post attributes" box.

You can't apply templates to custom post types in this manner. That will show up only if the post type is 'page' ( Check the wp-admin/includes/meta-boxes.php line 568 ). However if you want to style all your single custom post types in the same manner but different from other post types you could use the single-[posttype].php -> http://codex.wordpress.org/images/1/18/Template_Hierarchy.png

With my theme, I provide "virtual" templates. There are no specific {template}.php files in my theme, so I filtered the PAGE templates like so:

function my_virtual_templates( $templates ) {

    $my_virtual_templates = array(
        'virtual_template_id_1' => 'Template 1',
        'virtual_template_id_2' => 'Template 2',
        'virtual_template_id_3' => 'Template 3'
    );

    // Merge with any templates already available
    $templates = array_merge( $templates, $my_virtual_templates );

    return $templates;
}

add_filter( 'theme_page_templates', 'my_virtual_templates' );

I was looking for a "simple" way to add the actual post meta box on a Custom Post Type (CPT) when I came across this post. Since my new CPT will use this same array of "virtual" templates, I just needed to get a post meta box in place.

Using the theme_{$post_type}_templates It automatically creates this post meta box area for me. So where my CPT is called my_cpt I added the filter like so:

add_filter( 'theme_my_cpt_templates', 'my_virtual_templates');

Now, the meta box and selector shows up, and I can even change on the bulk edit screen since this is all built in. Very handy!