What magical language are you opposed to? The term "ritual" is pretty well defined: "Rituals are series of steps we take while attaching some kind of symbolic meaning."

In the article, they link to multiple papers they've written on the topic of rituals, as well as quantify their results in the experiment they performed:

"About 58% of the participants in our ritual condition chose the carrot over the chocolate, as compared to only about 35% of those in the control condition and 46% of those in the random-gestures condition."

As the article is in the magazine's "Behavior & Society" section the science in the article seems cogent.