Actually paper bags are worse than plastic bags. It all goes in the landfill (unless you recycle in which case it doesn't matter) and landfills are designed NOT to let stuff biodegrade. There are garbage excavations they've done into landfills which dig up readable newspapers from 50 years ago.
That being the case, plastic takes up less VOLUME than paper bags, so we can have more room in a landfill, thus plastic is better.
I imagine similar arguments could be made about game packaging.