It is not a war. The term you are looking for is 'terrorist threat', not war.
The propaganda you're spouting is really disgusting. Please read some CIA reports, analyses of jihadist groups, after-action reports from our soldiers in the field, and material produced by the Pentagon. Read the 9/11 Commission Report in full if you haven't already.
I am incredibly upset that American citizens are so poorly educated. This kind of reactionary fear plays precisely into the agenda of terrorist groups. It's as if people forget the derivation of the word.
Terrorist groups are loosely allied, poorly coordinated, as preoccupied with killing each other and various Middle Eastern governments as with attacking us, and (according to their own statements) fighting for what they perceive as their own freedom. The 9/11 attack, the most successful thing they've ever managed, was a series of pratfalls on both sides, not an insidious and well co-ordinated plot. It was, in short, a criminal heist, not an act of war.
(The entire plot was nearly uncovered because one of the attackers flew home to visit his girlfriend. Seriously.)
It is not a cultural war because Islamism isn't a culture. It is a radical aspect of a culture, in much the same way the Westboro Baptist Church or militia groups are a radical aspect of American culture.
Mischaracterizing the enemy will get you into further disasters. Don't do it.