Interactive Democracy gives more power to the electorate and less to the political parties. I suspect that this would cause a serious switch of political funding towards campaigns on issues and away from the traditional parties. But would this strangle them?
Political Parties are still important in the ID system. They contribute to Parliament and can become the government. So they still have influence and, I assume, would still garner support and funding. However, if a lack of funding became a major issue for the survival of the parties a debate could be raised about alternative methods of support. Something that has been done in many countries around the world.