The title The Gift of the Magi proves important to your question. The Magi who brought gifts to Jesus couldn't possibly know how important their demonstration of recognition for a savior was at the time.
Both Jim and Della gave literally the most important thing that they owned to each other. Their sacrifice was so tremendous that the outcome of the story proves that the gift wasn't what mattered, it was the gesture to be willing to risk all, or at least that material item at the time which meant the most to them. Likewise, I think this proves that items are not important at all, relationships are.