I haven't listened to this podcast before, but the guest is definitely a doomer so far (35 minutes in). I don't think nuclear weapons will be used on Iran. I don't know enough about the fertilizer and helium pieces but I do know that Iran is not going to give in easily. They want to make this as painful as possible so they are left alone in the future. I think the most likely outcome is that this is an ongoing "low intensity" war as long as congress lets him do it.
But for the segment you linked, yes, inequality causes war, because war is one of the easiest ways for the elite to release the social pressure valve without them having to give up much of anything in the short term, and they usually make a great deal of wealth as long as their country is not on the losing end.
War externalizes internal problems, takes attention away from the inequality, and kills off at least some of the poor all with the promise of the spoils of war for the general populace. The latter rarely benefit from spoils and when they do, it is very indirect.