Firstly, in the model the treatment is binary for all eligible households that choose to participate. However, there are large differences between participating households in the amount of awarded food stamps: For a two person household in 2016 the smallest possible monthly benefit was 16 USD while the largest was above 350 USD (\citealt{Lauffer2017}, p.103).  
Secondly, since they do not observe assets, their population of eligible children likely includes children that are not eligible because their households are too wealthy to be eligible. Assuming that such households would benefit less than comparable, less wealthy households, their estimated ATE is overestimated.