Lots of media outlets are ragging on Secretary of State Kerry for saying what we're about with ISIS is "not war." Here are examples at CNN, the Washington Times, and CBS News.
To paraphrase former President Clinton, it depends on the definition of "war." If by war you mean what we did in Kuwait or Iraq or Afghanistan, what the President plans to have Americans do to ISIS is not war.
Certainly, the President believes ISIS will experience the collective activities of the U.S. and its local allies as war. He hopes to have the troops on the ground be proxy forces - Kurds, Sunni tribesmen, and the Iraqi Army - instead of Americans. Whether he can find willing and, even more important, able local fighters to provide enough boots-on-the-ground is far from clear. I doubt it is possible.
Obama believes Americans are unwilling to send ground forces back into Iraq and into Syria. This belief certainly was accurate before the beheadings, it may or may not be true today.