Managed to sort it, the primary category is added as post meta to the post, therefore you can pass through the following arguments:
'meta_key' => '_yoast_wpseo_primary_news-category',
'meta_value' => 1179,
Note: your meta key will be different since this is a custom taxonomy that I have set up, if you print the get_post_meta for your posts, you should be able to see what the meta key is…