If we are to argue that the 1936 election was the most important since 1896, we must focus on the fact of the New Deal and the changes that it brought about in the relationship between Americans and the national government.
Before 1933, government had been a relatively hands-off thing. The federal government did not, for the most part, regulate the economy. It did not implement programs like Social Security to protect us in our old age or the FDIC to prevent us from losing our money if our bank failed. The government more or less left people to fend for themselves. This changed with the New Deal. Now, the government was seen as a guarantor of economic security for the people.
The 1936 election was important because it ratified this change. It is conceivable that the people would have looked at the four years of the New Deal and decided that it was a bad idea to expand government powers in this way. In that case, they would have voted President Roosevelt out of office and the New Deal would have died. As it was, they returned Roosevelt to office in a landslide. This confirmed the idea that the people wanted a more activist government, changing our nation in ways that are still important today.