It is probably the best possible result for Nazi Germany. It butterflies away the invasion of Russia and a DoW on the US. Though Stalin is building up his army, I doubt he ever attacks a major power such as Germany. Without a German invasion, his people are divided and Stalin is too paranoid of internal enemies to make new ones.
Being that Goering is the likely heir apparent and he was the head of the Luftwaffe, you probably see a greater emphasis placed on air power and bomber fleets, probably a great breuilding of the Luftwaffe after failure in the BoB. It probably butterflies away the blitz.
Italy is still in the war, so Great Britain gets to have fun beating up on them. Goering, for political reasons, will probably offer the Italians similar assistance as OTL. This means that Germany probably still projects its power into the Balkans due to the Italian failure in Greece.
By 1943, the British are probably fought to a stand still in Africa and by 1944 are beginning to face the new generation of German aircraft (He177, Me262, Ar234). The British may have lendlease, but not like OTL. THere won't be a blitz nor an invasion of Russia.
There is probably some sort of peace in 1944 due to economic reasons all around. I can't imagine both sides bankrupting themselves over domination of the North African wastelands, as this would be the only theater where there would be real conflict. Without US intervention, I imagine that economically there is only so long the British can fight rallying support to "liberate France" which in this ATL is a fool's errand.
Of course, the US can always end up joining the war anyway, but a leader intent upon lessening instead of increasing the conflict, it seems like a reach.
Finally, in this ATL, the question is what ultimately happens to the Nazis and to Germans. I suppose they hold on like the USSR. They would be in control over some pretty powerful economies, and being the uncontested military poer of central Europe, would probably end up having a Cold War with the Russians to keep the Hungarians, Romanians, and Italians in their camp. I can see the US offering support to either side depending upon which way the wind is blowing, so neither power gains supremacy in Europe.
However, when Goering or any immediate nazi-successor dies, they are not going to have the cult following that Hitler did. Hitler had the government organized in such a fashion so all roads led back to him. Whomever takes over after him will make tons of concessions and will have much weaker central authority.
Of course, there is always the threat of a military coup and Germany becomes a glorified south american country.
Germany would eventually lose its European satellites, including France, and exist today as a much larger country, probably retaining large parts of Poland, Luxembourg, France, Denmark, and the Czeck Republic that it does not today. GDP may or may not be equal, though I actually think it will be less because bombing a country into a ground so it has to rebuild all its industry does wonders for modernization.