Um, every single Muslim does believe in Jihad. It's an integral part of the Muslim religion and all its branches/denominations. Very liberal Muslims believe in Jihad just as much as traditional Muslims believe in Jihad. The very liberal Muslims tend to emphasize that Jihad can be of a non-armed nature whereas the more traditional Muslims emphasize the militant, sometimes armed, nature of Jihad and disagree with the modernist, liberal, watered down view. Jihad is an obligation binding on every single Muslim in Islam. So basically you've got an army larger than the army of China ... actually larger than the army of all non-Muslims countries combined! It's similiar to the situation in North Korea where everyone there is basically part of the army, ready to be called upon in a moment's notice.
Here's two VERY balanced articles that are very enlightening (especially the second one which will give a lot of history/sociology):
Maybe they aren't good Muslims from the perspective of SOME other Muslims, but that doesn't mean they are not Muslims. In Christianity there are groups that say certain other Christian groups are not Christian. For example there are some Christian groups that say that Catholics aren't Christian. That doesn't mean that in common discourse we should say that Catholics aren't Christian or that these very traditional Muslims are not Muslims.
