The political and military structure was certainly feudal, but it never really addressed whether there was serfdom, though the semi-sequels say the Tleilaxu use a strict caste system. What made feudalism realistic in Dune was the Holtzman shields, which made most non-melee combat impractical, and the Spacing Guild's monopoly on interstellar travel. The Guild didn't want the Emperor to centralize power and potentially threaten them, so they ensured most planets had to be effectively autonomous as fiefs. There's no reason the Dune universe couldn't have been largely democratic, though, except that there was strong political pressure for stability and hereditary autocrats were the obvious solution.
The big thing that made feudalism feasible in Dune was the lack of computer technology and the inability to advance non-cataclysmic military technology. In the Old Empire of the prequels, a handful of people are able to conquer everything except for remote vacation planets at the speed of communication, because technology is the great multiplier of potential violence and when the revolutions come, it's not the ability to spend money or persuasion that wins, but the ability to project and monopolize violence.
Again, this is poor 'ole Herbert not really understanding political systems. Hereditary autocracies are anything but stable. For a stable political system, you want a smooth transition of power between groups, particularly when there are changing power dynamics. If CK2 teaches us anything, succession in hereditary autocracies is anything but stable (and, to be fair, it's a dash more stable in the real world than in CK2, but if you look at the history of hereditary autocracies, it's not that much more stable). Plus, even in feudal times, it wasn't always strictly hereditary. In many cases, the king was 'first among equals', and if the king was out of line, then another noble would challenge and take the title. If Dune universe wanted stability, then a sensible, Westminster-style democracy would have actually been the best way to go (of the forms of Government we're familiar with at this stage). Of course, in the popular imagination, autocracies are more stable than democracies, but the historical record doesn't bear this out for well-structured democracies (ie, not Italy or Japan).
As for non-melee combat or melee combat, it's not the type of warfare that dictates the political structure - it's completely irrelevant. It's the range of power bases in society. In a society with a relatively small power base (land), feudal structures make a lot of sense, but once the economy develops further, it doesn't matter if one nation/planet is isolated from others, a one-dimensional political system won't be able to cope with a multi-dimensional economy and society in the long run. Even if there was serfdom, it still wouldn't allow for feudalism because there was so much more to the economy than basic subsistence (the bulk of economic activity in feudal times).
Dune's a great story, but it's broader political world doesn't really stand up to scrutiny. It shouldn't have to, it's a bit of fun, not a serious commentary on social or political structure - that's a backdrop to Atreide's adventure.