Read the full article at the link. The statute contains a cross-reference to a different statute which says that an "affirmation" can always be substituted for an "oath."
“The statute contains a cross-reference...”
No, the statue does not. Some legal software will provide you with cross references, and that helps to build a legal case. One can also look at notes provided by Congress for fuller explanation, when they exist. But those are things COURTS do. The military takes a law at face value.
An affirmation usually means you have a religious objection to swearing an oath, as I do.