Register custom page templates in WordPress programmatically in a plugin or in the theme without even requiring real template files.

class-templater.php

<?php
/**
 *
 */


/**
 * Class MCF_Templater
 *
 * Based on work by Harri Bell-Thomas <https://github.com/HarriBellThomas>
 * @link http://www.wpexplorer.com/wordpress-page-templates-plugin/
 *
 * @author Max GJ Panas <https://github.com/Maximilianos>
 */
class MCF_Templater {

	/**
	 * The array of templates that this plugin tracks.
	 */
	protected $templates;

	/**
	 * The directory where the templates are located
	 */
	protected $template_dir;


	/**
	 * MCF_Templates constructor.
	 *
	 * Initializes the plugin by setting filters and administration functions.
	 *
	 * @param array $templates
	 * @param string $template_dir
	 */
	public function __construct( $templates = array(), $template_dir = null ) {

		$this->templates = $templates;

		$this->template_dir = $template_dir;

		add_filter( 'page_attributes_dropdown_pages_args', array( &$this, 'add_to_wp_cache' ) );
		add_filter( 'wp_insert_post_data',                 array( &$this, 'add_to_wp_cache' ) );

		// interop with Advanced Custom Fields
		add_filter( 'acf/location/rule_values/page_template', array( &$this, 'add_to_acf_rules' ) );

		if ( $this->template_dir ) {
			// Add a filter to the template include to determine if the page has our
			// template assigned and return it's path
			add_filter( 'template_include', array( &$this, 'get_template_path' ) );
		}
	}


	/**
	 * Adds the templates to the pages cache in order to trick WordPress
	 * into thinking the template files exists where they do not really
	 * exist.
	 *
	 * @param $attributes
	 *
	 * @return mixed
	 */
	public function add_to_wp_cache( $attributes ) {
		// Create the key used for the themes cache
		$cache_key = 'page_templates-' . md5( get_theme_root() . '/' . get_stylesheet() );

		// Retrieve the cache list.
		// If it doesn't exist, or it's empty prepare an array
		$templates = wp_get_theme()->get_page_templates();
		if ( empty( $templates ) ) {
			$templates = array();
		}

		// New cache, therefore remove the old one
		wp_cache_delete( $cache_key, 'themes' );

		// Now add our template to the list of templates by merging our templates
		// with the existing templates array from the cache.
		$templates = array_merge( $templates, $this->templates );

		// Add the modified cache to allow WordPress to pick it up for listing
		// available templates
		wp_cache_add( $cache_key, $templates, 'themes', 1800 );

		return $attributes;
	}


	/**
	 * Adds the templates to the Advanced Custom Fields
	 * Page Template rule
	 *
	 * @param array $choices
	 *
	 * @return array
	 */
	public function add_to_acf_rules( $choices = array() ) {
		return array_merge( (array) $choices, (array) $this->templates );
	}


	/**
	 * Checks if the template is assigned to the page
	 * and makes sure to render the correct template
	 *
	 * @param $template
	 *
	 * @return string
	 */
	public function get_path( $template ) {
		global $post;

		$page_template = get_post_meta( $post->ID, '_wp_page_template', true );

		if ( ! isset( $this->templates[$page_template] ) ) {
			return $template;
		}

		$file = $this->template_dir . $page_template;
		return file_exists( $file ) ? $file : $template;
	}
}

True, doesn't work on 4.7.x either.