I agree that some caution is needed. If the definition of faith as he gives in the paragraph you quote is exactly as he sees faith it would be a radical departure from the truth.
But my impressions weren't centered on the specifics but from a general overall view of what he was saying. But such specifics should be tempered because otherwise they carry weight that can override one's central message. He shouldve tempered his definition of faith in that very sentence: Faith is belief in action. By leaving out belief he opens himself up to criticism and rightly so. The problem is that one can obey without trusting, one can work without trusting so therefore faith can not be a synonym for obedience or trust without the qualification of belief preceding action.
Faith is sometimes used in place of belief without the idea of action involved in the connotation. Faith is sometimes used as belief in action. Faith isn't in the Bible used as simply action [work, obedience, or any choice]. Even though he qualified it by saying, "in this sense", he made an error in seperating "unbelief" and "disobedience", but failed to include the counter to unbelief in his synonym of faith.
We do belief and confess. We confess with our mouth His Lordship. We confess with out time, and resources and fellowship that we are children of God. But others confess without belief and make false confessions. To equate faith with confession [good works, obedience] without mentioning the belief part is wrong.
My opinion is that we should be cautious but that Armstrong simply misstepped given the overall thrust of the article. But no preacher or treacher of the Word save those easy believism types has advocated that faith is jsut belief and works need not accompany it. They all preach that faith alone is never alone but has its foreordained works. So when some start trying to claim that others are preaching a faith that opposes works, I agree with you, red flags go up.