It's not a denial. The part I highlighted doesn't make sense to me. What does it mean? Would that not make US a failed state?
It is a shortened version of
"monopoly on legitimate use of force within its borders" i.e. only the state is allowed to use force within its own borders with it being accepted as necessary / legal etc
If a terrorist attack happens it is force within the state's borders, but it is not
"legitimate" force. When violence happens on a daily basis without being prosecuted or stopped in any way, like when the mafia completely runs a city for example, or like in South Africa where entire neighborhoods get shot up by gangs on a daily basis while the police do sweet f-all ... that inaction or inability by the state to stop
"illegitimate" violence means they no longer have a monopoly on violence.
Hence by the old, simplistic, definition we are already a failed state, our government is wholly unable or unwilling to stop illegitimate violence and have thereby given up their monopoly on violence.
The US, despite all its flaws, most definitely retains their monopoly on legitimate violence within their borders. Look at what happens when there's a terrorist attack? They wage unilateral war, that maintains their monopoly on violence.
A failed state would simply ignore it.