The original question was "Why do turbine engines require a compressor section", how did we get into diesel engines, pistons, turbo- and super-chargers?
The simple answer to this very straitforward queation is that a compressor, delivering high pressure air, is required to ensure self-sustaining operation. The compressor delivery pressure (and the velocity) at the inlet of the combustion chamber must be high enough to ensure that the pressure in the combustion chamber results in the combustion gasses flowing through the turbine section and and not 'backwards' into the compressor.