4E plays more like a board game because it doesn't require you to give the fictional content any weight.
I think this is the best attempt to explain why the game is like a board game, on the assumption that it is like one. But I don't entirely accept the assumption. I think 4e does require the fictional content to be given weight. This is obvious in non-combat situations: skill challenges, using rituals, general exploration, etc.
But I think it is also true in combat: positioning and speed, for example, are part of the fictional content, and they matter. At least in my experience, so are many of the properties of both PCs and NPCs/monsters - whether they're bloodied or not, whether they're big or small, whether they're wreathed in flames or not. These things all matter, and they're all elements of the fictional content.
Maybe "mattering" isn't enough to establish "required", however - because the rules establish these factors in rule terms alone, I guess you
could play the game without worrying about the fictional content that the rules are representing or mediating.
But then, in this case are you fully playing the game? For example, if you don't think about the fictional content that the combat mechanics are representing/mediating, then you're going to have trouble implementing various skills, especially Acrobatics, or anything that is based on DMG p 42. This is why I think it matters, in thinking about what 4e is as a game, and whether or not it is boardgame/MMO like, to consider all the elements of the game mechanics and not just chapter 9 of the PHB.
(Similarly, Burning Wheel's Fight! mechanics look like they could be deployed without having much regard to the fictional content being represented/mediated, but if you didn't pay attention to the fictional content then you couldn't use FoRKs in combat, and so wouldn't be playing the game in the fullest sense.)