To answer your question directly - he'll get the visa exempt stamp. Flashing the card will probably get him into the shorter "special" line but thats the extent of the benefits for US citizens.
US citizens arent eligible for the entry stamp. Each card on the back shows the countries the card holder may enter with his card and for US citizens this will always be blank. Imagine it kinda like being in the EU but opting out of Schengen. All other countries have reciprocal entry rights for card holders but the US didnt want to give up its immigration control.