I’d usually define “telling a story” to reflect the need for the document to be engaging, well-written, easy to read – and to have a clear overall message (”why us, why not the competition”). That certainly how it applies in a good Executive Summary.

Does that help?

This is entirely compatible with keeping it concise – indeed, if the proposal contributors have a clear ’story’ in mind, they’re more likely to keep material ‘to the point’ rather than hopefully throwing in anything that might possibly be of interest to the customer!