Except BK is an American company. They wouldn't operate in Russia if they weren't making a profit. So their net effect is to have money flowing out of Russia.

This is true. However, if I owned BK, I'd see this as an amazing business strategy, although a quite unethical one (but as we can see, multi million+ dollar companies aren't the most ethical either way). I mean, now the literal government has an interest for it to stay in business, they may even start to promote the brand.