OK. This is something of a teaser question designed to get students to really read and dissect the question.
1] When you see a question like this with an obvious/simple answer be very suspicious. After all surely every one knows who won the war so what's the question about. Not who won the war but how the war was won or in this case lost perhaps?
2] "Allies" is plural and used as a general or group noun. Hitler is singular and a specific noun; there only having been one Hitler (at that time).
3] It's also a "discuss" type question. This gives candidates a wide latitude for their answer provided, of course, that they can discuss/debate.
In fact Hitler got very involved in the management of the war right down to the micro-management level. He also had a very specific set of beliefs both in himself, particularly as a military leader and in his abilities to persecute a war. He also adopted a set of the goals for the war beyond the simple requirement to win. Leaders often do this but Churchill for example mostly confined himself to winning the war and crucially left the how to the military.
One of the most egregious errors was to invade Russia and therefore have to persecute the war on two major fronts. Additionally, notwithstanding the experience of Napoleon who also invaded Russia, he seemed not to understand the resource requirements involved. Armies need to be fed, equipped and transported. In this instance we can also add "properly clothed". The Russian winter was and remains 'a killer'. Large numbers of German troops simply froze to death. In addition much military equipment failed because of the cold. You cannot start a tank if the fuel is frozen in the tank! Apologies for the pun.
As a leader Hitler was intolerant of those (generals) that disagreed with him and simply replaced them. He also blamed failure on individuals rather than other, often perfectly reasonable and legitimate military reasons. This situation wasn't helped by his habit of surrounding himself with sycophants and "yes men".
The issue of the final solution introduces the problems of attempting social engineering while persecuting a war. Significant resources had to be set aside for this activity thereby weakening the war effort. The example here is that rail and transport considerations had a higher priority for this goal than military considerations.
He also personally interfered with Admiral Nimitz's submarine blockade of the UK preventing any long-term success.
Similarly in the air. It was Hitler's personal decision to switch the Luftwaffe from bombing British airfields to bombing London because he was outraged at a raid that had bombed Berlin. This gave the RAF time to regroup and meet the aerial threat. Remember the Luftwaffe had a 4:1 advantage in aircraft. British pilot losses were very very heavy but Hitler was unable to break their resolve. There is of course a modern contemporary parallel in the conflict now taking place in Eastern Europe.
You are however, quite correct in asserting that the Germans 'won' the first-half which strongly underscores the saying: "If you want peace - prepare for war".
This is a very interesting question generally but it only works for candidates if they know their stuff and can debate same. The Allies made a number of mistakes over the course of the war for various reasons but Hitler's role stands out as a primary case study.
So remember when you read examination questions think about them very very carefully to be sure you answer the question asked.