The game starts in 1936, because that's when a long series of events leading up to WW2 began (Japanese war in China, Germany breaking the Treaty of Versailles/annexing Austria/breaking up Czechoslovakia, etc...) This also allows for a degree of customization and individuality in your military. Do you want to have the USA utilize Soviet-style mass infantry formations? What about having the British use unrestricted submarine warfare? They'd be tough, but you can recreate your military and your doctrines in your own image.
The version I used for the above pictures is actually the expansion pack for HoI2, called Doomsday. It adds a lot of new technology to the end of the game allowing for skilled players to attempt to subjugate the entire world. To further facilitate this, the time limit was moved to 1953. In the original game, the time limit was the end of 1948, allowing for some events to occur ahistorically (Germany successfully defeating the USSR, invading Britain over the British Channel, having the Soviets take over all of continental Europe and spark an East/West war, etc...)
For all of its flaws, the game is actually the best at modeling that timeframe that I've seen. It's not overly complicated, but you need to understand what rules/effects/etc are in place in order to succeed.
But that's enough about that. If I make any significant progress, I'll relay it here. Now back to our regularly scheduled topic.