The "So Help Me GOD" portion is after the prescribed verbiage and not really part of the oath, but always present, much like when everyone cheers after the National Anthem is sung at a ballgame.
You can’t have it both ways.
The argument is that Obama did not say the oath exactly as written in the Constitution. The oath as written does not contain “so help me God”.
If the requirement is that the oath was be taken EXACTLY as written, adding “so help me God” is an issue as well.
It’s a really dumb argument.