The Nazis win. Keep in mind that the German military before rearmament was tiny, and had Nazi sympathizers in the ranks, as well as the officer corps.
The Nazis meanwhile had a massive paramilitary army in the SA, and loyalty of the Stalhelm would likely depend on the character of the military uprising. If this uprising comes from democrats loyal to Weimar, the Stalhelm will fight most likely with the Nazis. If its more of a Prussian Officer type coup, than more of the Stalhelm goes with the uprising.
Now, the HOI4 example comes somewhat later on (earliest in 1936). Once Hitler takes Austria, he will be popular enough to win such a Civil War. Indeed, after 1936, he was probably going to win such a civil war. However, in 1936, say the Rhineland annexation leads to a humiliating climbdown, eh, maybe there is more of a shot. After all, the SA had been cowed and the SS was still weak, and the German Officer Corps was still a bit hesitant about things.
Then there is the interesting impact on Nazi internal politics. Hitler largely curbed the more social revolutionary aspects of the SA in 1934, but Nazi leadership included some economic egalitarians and anti-Christians who might take things in a more radical direction if reactionary sections of the army rise in revolt.
I also find the map used in game to be a tiny bit off. Yes, initially, electorally speaking, the Nazis had their most amount of support in the East and in the North, but it wasn't exactly as clear cut as that. They did very well in East Prussia, Pomerania, and in the rural, Protestant areas of the North, as well as more urban, industrial areas of Saxony. But in the quite Catholic Bavaria, it was more like the Western portions of the country. The BVP and Zentrum were strong in each respectively. The Nazis I think would likely not have Bavaria, but would have a bit more in Northern Germany stretching a bit farther to the West, including the Holstein region, but not Hamburg. Berlin would likely rise for the opposition as well.