Savannah here from the Shopify Guru Team. :)
Great question! Media Mail is a specialty service offered by USPS and, although Shopify Shipping does integrate with USPS, it does not include specialty services such as this one quite yet.
You're more than welcome to submit a feature request for that option by emailing us at email@example.com. In the meantime, you could also calculate the Media Mail rate manually, and include it as a manual rate using this guide.
Let me know if I can clear anything else up!
Savannah | Shopify Guru