So quick question, does my MasterCard count as an official government-issued photo identification?

No it does not.

The hint would be govt. issued. Credit cards have nothing to do with the govt.

Acceptable are:

What are considered valid forms of ID? ...
Social Security Card, from the USA Social Security Administration, with your signature AND Photo Identification with your signature ie:

*unexpired driver's license *government issued identification card
*military identification
*or passport

Or you can go to any DMV office and apply for a photo ID that is not a drivers license.