If you read the article, it's not a binary true/false, there's a pile of conditions and assumptions that have to go into the comparison.
The actual study:
http://onlinelibrary.wiley.com/enhanced/doi/10.1111/jiec.12181/
Points out the break even point is 1.3GB (meaning Digital has less of a carbon impact below that point than disk), the study is based around UK power and distribution, and the study only looked at initial distribution, not life cycle. Life cycle for a digital game is basically 'download and it's over', whereas a physical disk will still have an existence later that could either be benign (gets traded and replayed forever) or bad (goes into the garbage bin).
Places with more renewables in the mix would lean towards download more, and flip that for less renewables. For the US, the average mix would be pretty worthless as it swings a lot depending on where you live.
In other words, it's complicated.