A real fire is not like the diagram: The various stages shown take place in a chaotic and constantly changing way and cannot be individually controlled.
Gasification and pyrolysis plants are based on the principle of separating out the processes that happen chaotically within a fire; seeking to perform them individually in a fully controllable manner. The extent to which these processes are separated and controlled characterises the various types of pyrolysis and gasification systems.
Some are very simple, e.g. an updraught fixed bed gasifier where only the final combustion of the gas above the fire is separated and done elsewhere.
Others are complex, with separate drying, pyrolysis, gasification and combustion stages all performed in different but interlinked equipment.
The final result is however the complete oxidation of carbon and hydrogen to carbon dioxide and water, hopefully with the maximum output of useful mechanical work, just as in a conventional combustion plant.
As with any other aspect of engineering, there are trade-offs to be made, and each process design has its strengths and weaknesses.
Crude gasifiers can only burn the poor quality gas in a boiler to drive a steam cycle and are not much different from a straight combustion plant.
More complex systems are able to separate the pyrolysis stage completely, producing a gas suitable for a more efficient prime mover such as an i.c. engine or a gas turbine. The trade off is that the thermal losses involved in the separation of the processes, and from the cooling and cleaning of the gas accounts for much or all of the prime mover efficiency gain.
The real strength of a gasification system is improved applicability at small scale, and the elimination of an expensive and inflexible steam Rankine cycle.
Controlling each stage of the combustion process individually and separately has some advantages in emission control; for example, charcoal residue from pyrolysis can be burned at realtively high temperatures without excessive NOx production, as all the fuel bound nitrogen is removed in the pyrolyser.
Advanced thermal treatment? It IS combustion - but not as we know it!