Why does the original Nintendo take 9V AC instead of 9V DC?
The NES requires a 13V and a 5V supply. The details are in the schematic:



full schematics and image source

The 13V supply is used for the video and audio outputs where 5V would not have provided sufficient headroom, especially considering the less sophisticated electronics of the day.

These days we take regulated supplies as the norm because switching supplies are cheaper (by eliminating the need for a large transformer), but that wasn't true in 1983. Then, the cheapest power supply you could get was just a transformer, which means AC output. While they certainly could have selected a wall wart that rectified and filtered to output DC, there just wasn't much to be gained. Since there was already a need for a power board to generate 13V and 5V, the cost of sticking a rectifier and a few extra capacitors on it is very small, and there's plenty of room in the NES for them to fit.