It's the most densely populated municipality in North America. I highly doubt it qualifies as suburban.
Guttenberg is purely a dormitory town, and as such could not of course be anything but a suburb. (That's part of the reason for the pop. density - no commercial or recreational areas to speak of.) Population densities and voting patterns and income levels have nowt to do with it, really.
But Guttenberg's commercial areas are right next door in West New York. You're looking at each municipality in isolation, which is a stupid way of doing things. There are much larger areas in Queens, for example, that are purely residential and identical to Guttenberg, yet you would call them urban because of arbitrary lines on the map combining them with the rest of New York City. Guttenberg is an urban residential area; the fact that it was made independent in the early 20th century doesn't change that.
Actually I do consider Queens and even southern Brooklyn to be inner suburban areas (South Jamaica is a suburban slum estate - heck, it even
looks like it must be in Seine St Denis on photos) , but that's neither here nor there really.
But the question of local government may or may not be a relevant one depending on the setup of local government. If the central city in fairly small and the areas around it are all in fairly large municipalities (as in Brussels, say) obviously it can't be used as a factor in determining what is and what is not a suburb. If local government is essentially powerless, it can't be used as a factor in determining what is and what is not a suburb. I don't think either case applies here. The boundaries of cities actually shape the settlement patterns. The absence of prestige municipal expenditure and of outsiders using the city's services shapes its tax burden. Etc.