A call to list all Custom Post Types?

You’ve to take a look at the documentation to know how to use a function, you can’t just replace them. If you do that you’ll see get_post_types() has to be used different then get_categories(). For example you can’t use the parameter hide_empty. Besides that you have to change the $output parameter to objects, default is names. There are many other possibilities for customizing your output, if you make use of the $args and $operator parameter. A basic untested example based on what you’ve tried so far is below.

Code:

$args = array(
    //  public - Boolean. If true, only public post types will be returned. 
    'public' => true,
    // _builtin - Boolean. 
    // If true, will return WordPress default post types.
    // Use false to return only custom post types. 
    '_builtin' => false
);
$output="objects";
$operator="and";
$cpt_post_types_obj = get_post_types( $args, $output, $operator );
$cpt_post_types = array();
foreach ( $cpt_post_types_obj as $cpt_apt ) {
    $cpt_post_types[] = $cpt_apt->name;
}
$post_types_tmp = array_unshift($cpt_post_types, "Select a post type:");

---

Update:

As the constructing of the custom post type array works with above code, the problem might have to do with your dropdown. Below an example how you can do it.

Code:

echo '<select name="post_type_dropdown">';
    foreach ( $cpt_post_types_obj as $cpt_apt ) {
        echo '<option value="'. $cpt_apt->name .'">'. $cpt_apt->name . '</option>';
    }
echo '</select>';

---

2nd Update:

Like I said, it’s working for me. Use below code, just put it into your functions.php to test, debug it.

Code:

add_action( 'init', 'wpse132165_pt_list_debug' );
function wpse132165_pt_list_debug() {
    $args = array(
        //  public - Boolean. If true, only public post types will be returned. 
        'public' => true,
        // _builtin - Boolean. 
        // If true, will return WordPress default post types.
        // Use false to return only custom post types. 
        '_builtin' => false
    );
    $output="objects";
    $operator="and";
    $cpt_post_types_obj = get_post_types( $args, $output, $operator );
    // open up the next line like this /** to comment the code until the next /**/
    /**/
    echo '<pre>';
    print_r($cpt_post_types_obj);
    echo '</pre>';
    /**/
    $cpt_post_types = array();
    foreach ($cpt_post_types_obj as $cpt_apt) {
        $cpt_post_types[] = $cpt_apt->name;
    }
    /**/
    echo '<pre>';
    print_r($cpt_post_types);
    echo '</pre>';
    /**/
    echo '<select name="post_type_dropdown">';
        foreach ( $cpt_post_types_obj as $cpt_apt ) {
            echo '<option value="'. $cpt_apt->name .'">'. $cpt_apt->labels->name . '</option>';
        }
    echo '</select>';
}