The authors were asked about potential reasons, and responded with:
There are many pathways potentially linking family economic circumstances and brain structure and function, and we are very interested in two of them. The first is the investment, or “what money can buy,” pathway. Parents with more resources can buy more books and toys, afford better child-care experiences, provide housing in better neighborhoods, and provide better learning opportunities inside and outside the home.
The second possibility is the family-stress pathway: Families facing economic strain often deal with stressors that are associated with less responsive and less warm parenting. If the parents are very worried about how to keep the lights on, or they have to work that third job, they’re less able to be present with their kids.
I suspect it's a combination of the two.