single.php

$post = new TimberPost();
$context['post'] = $post;
$category = $post->category(); // this will be a TimberTerm assuming there's 1 or more category assigned to this post
$query = array('posts_per_page' => 6, 'cat' => $category->ID, 'post__not_in' => array($post->ID));
$context['latest'] = Timber::get_posts($query);

//the rest as you had it in your gist