The meaning of the word 'inert' is 'not moving'. In the excerpt, it is described that the machines were not moving, as if they were dead. The word 'inactive' has the same meaning - it stands for something that is not operating, moving or is out of function. This is why we could replace 'inert' with 'inactive' in this example.
The main idea of “The Gift of the Magi” is that the value of a gift is in the giver, rather than the gift itself. Jim and Della, out of their love for each other, purchased a gift that required them to sacrifice something that was precious to them.