A paradox is defined as "a statement that is apparently self-contradictory or absurd but really contains a possible truth."
Jim and Della were not rich in the sense of material possessions. They did not have lots of money; indeed, Jim's pay had been reduced by one-third, from $30 to $20 per week, at some time before the start of the story. As a result, they lived in poor housing and had very little to spend for food or possessions.
she had only $1.87 with which to buy Jim a present. She had been saving every penny she could for months, with this result. Twenty dollars a week doesn't go far. Expenses had been greater than she had calculated. They always are.
However, Jim and Della were rich beyond measure in affection for each other. They were one of the richest couples on earth in the sense of having the complete devotion of their partner to treasure, a gift that is valuable beyond measurement in dollars. "Eight dollars a week or a million a year - what is the difference?"
Being rich doesn't always mean having lots of money, but that's what most people think of first when someone is described as being rich. This is what makes your statement a paradox.