To me, an automat has to be one where you put your money in and get your food right away. Eatsa was more of a fast food restaurant, but you got your food in a cubby rather than at a counter.

The last true automat I've seen in the US is one in Manhattan that I visited around 2008 (I think it was called Bamn!). It was, truly, nothing more than a novelty. The food wasn't good at all.