I would like to know how to sort this list of categories (I followed this tutorial here http://www.devinrolsen.com/magento-custom-category-listing-block/) in magento by posi
If you want to sort the categories by the position created in adminhtml you can then, since catalog/category is an instance of Mage_Catalog_Model_Resource_Category_Collection, make a query where you specify what you want to select, filter and/or sort.
The case here is getting categories from catalog_category_entity select only the name, filtering after the id and sort the query on the position.
getCollection()
->addAttributeToSelect('name')
->addFieldToFilter('parent_id', $categoryId)
->addAttributeToSort('position', ASC);
?>