How to check payment method on a WooCommerce order by id?

The post meta key for the payment method ID is simply _payment_method

So if $order->payment_method doesn’t have the magic methods in place to get that automatically, you could retrieve the post meta using traditional WordPress

get_post_meta( $order->id, '_payment_method', true );

Update for WooCommerce 3.0

$order->get_payment_method();