as /u/true_new_troll pointed out basically there's no way to answer this without challenging the assumptions implicit in the question.

For instance, is there a direct link between intervention, hatred, and terrorism? What defines intervention? Does US material support for Israel count as "intervention" in the 1967 and 1973 wars?

Part of the issue here is that there was an almost unique political situation where some of the largest, most politically active countries in the middle east aligned against the United States and therefore had much to gain by blaming the United States for supposed interventions. Nasser, for instance, claimed that the US had directly intervened in 1967, which was simply untrue.

The other issue is that as much as the news likes to describe "the Middle East" as a contiguous region, this question is a little bit like a middle eastern observer asking in 1950 why it is that constitutional monarchy has led to the total destruction of Europe in two major wars. You can talk about regional issues between powers but there are supremely local issues that you have to separate out.

For instance, prior to about the 1980s if you were to talk about international terrorism in the Middle East you'd be talking about radical far-left hijackings carried out by the PFLP. In the 1980s you'd be talking about (against the US and France) the bombings carried out by pre-Hezbollah Shia terror groups in Lebanon (the embassy and barracks bombings). And not to get into 20 year territory but obviously the ideology of Al-Qaeda is completely different and essentially unrelated to those groups.

And of course we could separate this out to countries that have been subjected to terrorism other than the United States. The FLN carried out what can very easily be described as a terrorist campaign against the French (of course I think it's entirely possible given the policy of mass reprisal that you could characterize the French military campaign as a terrorist one as well.)

Or possibly the oldest terrorist campaign in the middle east, the Zionist Irgun organization. Uri Avnery, who is still alive and to a certain extent active in Israeli politics, has been quoted as saying "You can't talk to me about terrorism, I was a terrorist." Menachem Begin's "The Revolt" makes it pretty clear that he was essentially operating as a terrorist, and he believed it was justified.

Are these forms of terrorism somehow interconnected and unique to the middle east? To its politics? To its culture? To its religion? etc.

I would seriously doubt it.