Could also split that out into different files to be loaded on the applicable page(s) instead of always loading that css on every page:

If you create a file in includes/templates/YOUR_TEMPLATE/css
named:
checkout_payment.css
checkout_shipping.css
checkout_confirmation.css

With the applicable css to apply when just that page is shown.

So in checkout_payment.css could have the above:

#checkoutpaymentBody .rightBoxContainer {display: none;}