Solved it by changing a minor thing in the query, thanks to peterm!
The new query:
SELECT `products`.*
FROM `categories` AS `node`
JOIN `categories` AS `parent`
INNER JOIN `products` ON `node`.`id` = `products`.`category_id`
WHERE `node`.`lft` BETWEEN `parent`.`lft` AND `parent`.`rght`
AND `parent`.`id` = '1'
ORDER BY `node`.`lft`;
Using a jon