Hezbollah indeed unites the shia community in Lebanon, but the Lebanese brand of this religion is not quite the same as the Iranian one. Meanwhile, three other organizations mentioned here are NOT shiite at all, but sunni based organizations. As to the PFLP, it is secular, or rather, atheist. Whether Iran provides weapons to any of these, I actually don't know. I don't believe I've seen proof. On the other hand, what stands out from the list you supply is that the Iranian leadership is quite PRAGMATIC: it supports forces based on their POLITICAL STAND, and not on "religious leanings".
The question ought to be then: what is the political stand which Iran supports? The first thing to note is that the list of forces mentioned in this quote is not exhaustive. Iran seems to have no problem with China, for example. I don't recall any public spats with Russia either. And Iran seems to have had good relations with its neighbors Iraq and Afghanistan, through most of the last few years, in spite of the fact that both of them are under American occupation. The relationship with Armenia seems to have been cooperative since it became independent.
More interesting, perhaps, is its growing friendship with Turkey. Turkey's denunciation of Israel during its war in Gaza in early 2009 was widely commented on. For many people it seems to have marked a turning point in that country's evolution. In fact, it seems to mark a new resolve to stand up to the West, at least symbolically. One Iranian leader (I don't remember which) remarked at the time that THIS was what was meant back in '79 or the early '80s when Iran said it wanted to "export" the Iranian revolution. They did not want to replicate subversion and revolution; they wanted states in the region to stand up to the West, and particularly the US and the UK.
This example is interesting because it isolates just what Iran is seeking in its foreign policy. Iran wants to end Western, and particularly American, domination of the Middle East. For the reasons, you have to look at history. I don't want to do this here, but I will say that on this question the views of the Iranian regime are much more representative of the views in the street in the Middle East, both Persian and Arabic, than are the states and forces which are "friendly" to the West. Polls conducted late in 2006 in several countries found that Ahmadinejad and Nasrallah (the leader of Hezbollah) were by far the most popular political figures in several of the Sunni Arab countries at that time.
@jantxv: On the specific forces mentioned in your list, it should be noted that all of them are political actors within Palestine/Israel and Lebanon. All of them have also been labelled "terrorist" as well, and I think the gist of your examples is to cast Iran in a certain light. But it is also true that both of these places have been in a constant state of insecurity and on/off civil war for many decades. These problems are MUCH OLDER than the Iranian revolution. The last American intervention in Lebanon predates Iranian influence there, any all of Israel's wars involving Arab states predate the Iranian revolution. In this case, the Iranian regime is simply taking a stand on problems that were there LONG BEFORE they were. They certainly did not CREATE the problems. And in this stand of theirs, they are the ONLY major state in the Middle East that actually actually speaks for the majority. In other words, YOU may see them as "terrorist" organizations, but for most people in the Middle East, they are heroes. The Iranian regime sympathises with these organizations because, in the context of these nearly constant civil wars in these places in the last several decades, these are the forces which, in their view, take the most consistently uncompromising positions against outside encroachment.
