Which General Staff member directs management of all incident-related operational activities to achieve the incident objectives?

The General Staff member responsible for directing the management of all incident-related operational activities to achieve the incident objectives is the Operations Section Chief.

The Operations Section Chief’s role within the Incident Command System is integral to the successful management of emergency responses. This position requires a deep understanding of the incident’s complexities, the available resources, and the necessary tactics to address the incident effectively. For instance, in a large-scale wildfire, the Operations Section Chief would oversee the deployment and actions of ground crews, aerial resources, and any other assets engaged in firefighting efforts. This individual coordinates the efforts of different divisions and groups, ensuring that operations are conducted safely and contribute directly to achieving strategic goals.

Source: https://training.fema.gov/emiweb/is/is200c/english/instructor%20guide/is0200c%20ig.pdf