First of all, I’d say that the non-intentionalist side of the debate is more often referred to as the “functionalist” side of the debate and that it has less to do with the structure of the Nazi Party specifically but rather of the Third Reich generally.

The functionalist approach, like the intentionalist approach, has hard and soft versions. Whereas a hard intentionalist, arguing for a straight line from Mein Kampf to Auschwitz, would include someone like Lucy Davidowicz, compared to softer approaches from the likes of Andreas Hillgruber and Peter Longerich, the functionalists range from harder approaches like that of Götz Aly, who argues for a sort of “Holocaust from below,” to someone like Christopher Browning, who argues for something he refers to “functional intentionalism,” which envisions a functionalist origin with an intentionalist conclusion.

Another thing to bear in mind is that this is a mostly resolved debate, at least among qualified historians. Browning’s version of events has proved the best supported by evidence over time. In short, Hitler is often misunderstood as a person controlling minutiae from above, whereas per Martin Broszat and others, he was a “weak dictator,” who established a broadly flung bureaucracy to carry out vaguely enunciated goals. This is what Ian Kershaw refers to as “working towards the Führer.” The route that Browning traces goes from a policy of emigration through the beginning of the war to one of concentration and waiting for later expulsion during the Polish campaign. With Barbarossa, explicit instructions were given to execute Jewish men 15 to 50 years old, but with “cumulative radicalization” on the ground and the independent initiative of men in the field in the USSR, the result was the destruction of whole Jewish communities by the late summer 1941. As prospects of a short war dwindled and the General Gouvernement became packed with Jews deported from the Reich, opinions turned toward extermination of all Polish Jews in concentration camps using poison gas, following ad hoc experimentation in the field and the conclusion that mass shootings took too heavy a toll on personnel. This decision likely came in fall 1941, with the remainder of European Jews condemned at that time or shorty thereafter. Surely by the Wannsee Conference on 20 January 1942, the die had been cast.

That said, once coordinating meetings like Wannsee are being held, it’s hard to argue that the approach being taken is not intentional. However, there is little evidence that Hitler participated in these decisions more than being informed of them. The buck basically stopped at Himmler, with Heydrich sweating much of the details and, in programs like Aktion Reinhart, functionaries like Odilo Globocnik operating with little oversight.

I’d strongly recommend Browning’s Origins of the Final Solution for a very through overview of this process. He also deals pretty well with the shortcoming of the intentionalist theory.