General Electric gas turbine engines work on all the normal principles of physics you are taught in college engineering school. I don’t need to consult with a relative of any kind as I am, personally, a federally certified gas turbine engineer. There are some gas turbine powered, government owned, military ships in service that I have personally worked aboard many times. A gas will always flow from a higher pressure towards a lower pressure. Figure 1-2 on page 2 would be a more relevant diagram illustrating how a gas turbine works. The compressor blades are spinning, and this accelerates the air. This air mass acceleration is a source of the turbine engine’s forward thrust. Where does the compressor get its power to accelerate the air? You can see it’s via the shaft connecting the compressor with the turbine. The turbine is powered by the released energy of the burning fuel inside the combustion chamber that is then routed past the turbine blades to provide power to the turbine/compressor shaft. The exhaust from this operation is then expelled through the propelling nozzle. The nozzle will provide a little more forward force because the exhaust gases are accelerated when passing through the nozzle. The net force will be in a direction opposite the incoming air flow.
These gas turbine engines will require atmospheric oxygen for fuel combustion where rocket engines do not. The rockets carry their own oxygen with them inside. Both rockets and turbines provide forward thrust in the same manner, however. Both rely on accelerating mass to provide an equal and opposite force. Newton’s law never specifies what the mass must be. In a turbine engine, it’s outside air and combustion products. On a rocket its all combustion products. On a ship or a boat water is accelerated by the propellor to provide forward thrust.