Again, not what the definition of "mental illness" generally means.

Look up an actual definition or this

Can "terrorists" have mental illnesses?, sure.

Are all "terrorists" by definition mentally ill, doubtful.

Without even getting into the subjectiveness of the term "terrorist", lets take your example.

There are plenty of situations where you can end up with that point of view and not have a legitimate "mental illness", because that term means something relatively specific and isn't a good enough fit with which to broadly paint all members of a group.

Another example of why it doesn't fit is that there are plenty of people who are evil/bad/morally bankrupt (for whatever frame of reference you are using to determine such things) that shouldn't get to use mental illness as an excuse for doing shitty things.