Wordpress - How to retrieve all post titles of a specific post type?

You could - and in my mind, should - use API functions to get the data.

// query for your post type
$post_type_query  = new WP_Query(  
    array (  
        'post_type'      => 'your-post-type',  
        'posts_per_page' => -1  
    )  
);   
// we need the array of posts
$posts_array      = $post_type_query->posts;   
// create a list with needed information
// the key equals the ID, the value is the post_title
$post_title_array = wp_list_pluck( $posts_array, 'post_title', 'ID' );

Query all post titles of a specific post type

// Function that returns post titles from specific post type as form select element
// returns null if found no results.

function output_projects_list() {
    global $wpdb;

    $custom_post_type = 'page'; // define your custom post type slug here

    // A sql query to return all post titles
    $results = $wpdb->get_results( $wpdb->prepare( "SELECT ID, post_title FROM {$wpdb->posts} WHERE post_type = %s and post_status = 'publish'", $custom_post_type ), ARRAY_A );

    // Return null if we found no results
    if ( ! $results )
        return;

    // HTML for our select printing post titles as loop
    $output = '<select name="project" id="project">';

    foreach( $results as $index => $post ) {
        $output .= '<option value="' . $post['ID'] . '">' . $post['post_title'] . '</option>';
    }

    $output .= '</select>'; // end of select element

    // get the html
    return $output;
}

// Then in your project just call the function
// Where you want the select form to appear
echo output_projects_list();

For an hierarchical post type, we have the built-in:

wp_dropdown_pages( 
    [ 
        'post_type' => 'page',
        'echo'      => 1, 
        'name'      => 'wpse_titles', 
        'id'        => 'wpse-titles' 
    ] 
);

that will generate a select element with post titles and the post ID as the option value.

Example:

<select name='wpse_titles' id='wpse-titles'>
    <option class="level-0" value="1">AAA</option>
    <option class="level-0" value="2">BBB</option>
    <option class="level-1" value="3">&nbsp;&nbsp;&nbsp;CCC</option>
</select>

It's not clear from the documentation for wp_dropdown_pages(), but it's a wrapper for get_pages() and also support it's input arguments.