The article was covering a proposal by Rep. Phil Roe, R-Tenn., to hold SNAP beneficiaries to higher health standards along the lines of the Women, Infants, and Children (WIC) program, and the erroneous claim has since been repeated.
The study, from Yale's Rudd Center for Food Policy and Obesity, says something quite different:
"Researchers found that 58 percent of all refreshment beverages purchased by SNAP participants were for sugar-sweetened beverages such as regular soda, fruit drinks, and sports drinks. According to the researchers, SNAP benefits paid for 72 percent of these purchases." [Emphasis added]
The Yale study found that "SNAP was estimated to pay at least $1.7 to $2.1 billion annually for sugar-sweetened beverages."
Though reasonable people may conclude that is too much money spent on soda, it is not "more than half" of the roughly $80 billion in SNAP benefits paid annually.