Correct me if I'm wrong, but isn't the East Empire Trading Company operated under an Imperial charter? Why are they allowed to continue to operate out of the port of Windhelm while it is under Ulfric's control?

because without having an organization doing Imports and Exports any economy is doomed

Hypocrisy (or pragmatism, depending on how generous you are feeling) will get you far in the world. Ulfric probably tells himself and his followers that, while the East Empire Company is supported by the Empire, they are not necessarily an official, hostile part of it. And they can bring commerce to Windhelm that the city seems to desperately need. So, they can be viewed as a tolerable evil that serves the greater good.

To be fair, said followers (generic guard dialogue that does not differentiate between Imperial/Stormcloak aligned guards, anyway) don't seem to mind the PC helping said company wipe out a pirate gang either, and even thank them for it. The EEC still trades with territories that are no longer Imperial aligned either, so he's hardly unique in this.

Really, the only ones that aren't happy with the company is Raven Rock, and for good reason.

The real answer is that Eleveneleveneleven meant some quests got cut or the gameworld was just otherwise simplified. The EEC in Windhelm was one such casualty.

But, taken as is, I like to think it reveals that The Empire isn't necessarily the territory of the government apparat in White Gold, but a wider cultural superstructure that transcends national boundries, rather like the historical relationships of France or the Italian city-states with the Roman Papacy.

Even if the EEC had its charter revoked, given that it is such a huge company to begin with, Cyrodiil would only be shooting itself in the foot. The EEC very much appears as an equal opportunity corporation that will trade with anyone, as long as there is coin and profit to be made.

Plus, by opening EEC trading routes to Windhelm, the EEC continues to make more money, and Ulfric gains more goods and commerce into his city. It's a win-win for both sides.