Question: So in Dungeon World, there doesn't seem to be any stat for initiative or any structure to the sequence of moves that people can make. Is the game intended to be simply played "round robin", or do some people tend to make entire series of moves in a row, or what? I'm coming from games like D&D and Pathfinder, so the absence to a structure to the combat turn order is both refreshing and confusing.

Answer: 
It's up to the GM to direct turns in combat by switching between characters, often by asking "What do you do?"

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> The easiest question to use is "What do you do?" Whenever you make a move, end with "What do you do?" You don't even have to ask the person you made the move against. Take that chance to shift the focus elsewhere: "Rath's spell is torn apart with a flick of the mage's wand. Finnegan, that spell was aiding you. What are you doing now that it's gone?"
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The Example of Play chapter also demonstrates these transitions.

I suspect the same character making multiple moves in a row is boring and goes against the **fill the characters' lives with adventure** agenda.
I try to imagine the narrative of combat as being a bit like a soccer game. The spotlight is passed back and forth and sometimes intercepted. You want to make sure that everyone gets a chance, but remember, the GM's mandate is to always ask "What do you do?" and to be curious about the situation. Think about who each action might affect and ask them how they respond. Luckily, you only have half as many active members of a battle to think about - the monsters only go when the PCs look to you as if to say "well, what does the Ogre do now?" or when moves indicate they get to do something. The players will pick this rhythm up and start jumping in to have their say, too.