In the early part of the Industrial Revolution the rewards of increasing productivity went disproportionately to capital; later on, labour reaped most of the benefits. The pattern today is similar. The prosperity unleashed by the digital revolution has gone overwhelmingly to the owners of capital and the highest-skilled workers.
The skills that can't be automated (critical thinking, creativity, etc.) afford higher wages, increasing the income gap. The Economist argues that that income also brings mobility, which means the gap can't be closed by re-distribution of wealth.