It appears to be two actions, honestly much to my surprise.
You can take a move action in place of a standard action.
So when you do that, you get two move actions. You can use both to move up to your speed, as separate actions.
Nowhere under full-round actions is any mention made of a double-move action. Running and charging, yes, but not the simple double-move.
Now, Swarm Attack reads as follows:
they deal automatic damage to any creature whose space they occupy at the end of their move (no attack roll needed).
I read “their move” here to be “their move action” rather than “their movement.” I do this because, grammatically, “move” is not really short for “movement,” while having an implicit noun for an adjective (i.e. action for adjective move) is quite common in English.
So yes, this would trigger Swarm Attack twice.
However, it’s always good to acknowledge ambiguities in the rules.
Should it be run this way?
I’m not sure. I’ve never seen it run that way, and I sort of doubt that most swarms were designed with that ability in mind, but I could be wrong; after all, I was wrong about this working in the first place. In any event, just because the authors intended it one way doesn’t mean that’s how I want to run it in my game.
For my games, I’d have to carefully consider the swarms I was or was not using, and what options my players had for dealing with them, in order to determine how I would rule this. In my experience, swarm damage tends to be low, but at the same time the majority of character classes have almost-zero ability to do anything to them.
So, for example, if my party consisted primarily of mundane classes, I really would not make swarms twice as dangerous as I thought they were, because I already considered them too dangerous by virtue of their effective invincibility. So, and I suppose it’s a houserule considering RAW, I would not allow swarms to double their swarm attack damage by double-moving.
On the other hand, if I was making a campaign centered around swarms, and expected my players to build specifically with swarms in mind, I probably would go ahead and rule this as RAW, and let swarms do that. This would allow the swarms to be more of a threat for situations where the players aren’t just enduring them, but are actively and effectively killing them. It would also open up a few more tactics for dealing with them, such as partial action denial, à la Nauseated.
If I anticipated swarms being an issue either way, I’d make a point of informing my players of this issue, since it’s unlikely that any of them have considered it on their own.
As for “verisimilitude,” or “seeing it through the game world’s lens” or whatever, that doesn’t really come into play here: swarms are explicitly an abstraction, particularly with respect to the Swarm Attack (using one lump sum rather than thousands of minuscule attacks), so it’s really impossible to say what makes more sense in-character; in-character, a completely different thing is happening.