This is an interesting question. Hitler is obviously the central figure in the Nazi story, but Goering is a major figure too. Remove him... Hitler credited him with making something of the SA in the 1920s. How important was that? However it was before the Putsch, so it is OT.
Goering was important in keeping the NSDAP in business in the 1920s. As the "Salon Nazi", he raised money from the upper classes and provided a respectable face for a party notorious for street fighters. During the 1933 seizure of power, Goering was in contact with Hindenburg's circle and helped negotiate the terms of Hitler's appointment as Reichskanzler. He became Minister without Portfolio. He took charge of "Nazifying" the police, which were employed in the post-Reichstag Fire crackdown on the Communists.
If there is no Goering; the NSDAP probably veers more radical. Without him, Hitler and the Nazis may appear too radical for Hindenburg's circle, and remain stonewalled from power. The constitutional crisis continues, and Hitler may decide that he must gamble on seizing power by force, employing the huge number of SA men. If that gamble succeeds... the new regime will be very different from OTL.