As strange as it may seem, the United States actually has a precedent for declaring war against groups ¡Ìeven vague, nebulous groups- rather than nations. Here's the precedent: Two centuries ago, piracy was a constant threat to American ships and harbours. So much so that the Constitution laid out parameters for their punishment.
In 1801, under this article, the American Congress authorized President Thomas Jefferson to send the U.S. Navy to fight the Barbary pirates along the coastline of northern Africa. These pirates weren't a nation, didn¨t have a capital, national anthem, or embassy - but this made no difference.