I've heard it said in this sub that feudalism did not exist in the medieval period of Europe.

It didn't exist in the medieval period at all. You can read detailed explanations about why medieval historians believe this elsewhere on this sub (check the FAQs and my own post here). In short, there are two main reasons: firstly, the idea that there was any sort of 'system' or rationale behind the way in which medieval society and politics was organised isn't supported by the evidence. On the contrary, medieval society was very ad hoc, with political arrangements being made very much based on local circumstances. Secondly, in the past historians have never really come to any sort of consensus as to what 'feudalism' means, and so it can really mean whatever any historian wants it to mean at any given time.

What word would one use to describe their governmental system?

I don't think there's any one way to describe the governmental system of an entire continent over the course of a millennium, or even a couple of centuries. Like I said above, the political arrangements varied not only across the continent, but also across time as well. It would be a bit like trying to find one term to describe the the governmental system of the modern 'West'. Sure, we could say 'representative democracy', just as for medieval times we can say 'de-centralised monarchy' perhaps, but does that really describe them in any real way? I mean, the USA's two-party bicameral presidential republic and Denmark's multi-party unicameral constitutional monarchy aren't really the same political system are they? So we can really only say that the political systems of the medieval world were the same in the very broadest of senses.

Does feudalism describe any historical governmental system?

Like I said before, it's incredibly difficult to get historians to agree on what feudalism actually is, let alone whether it describes any actual historical situation. I'm one of the few medievalists on this sub who still thinks that feudalism has a place in medieval history, but I believe it is better seen as an ideal type, an imaginary model to which we can compare our evidence, rather than saying that such-and-such society is 'feudal'. But no, I don't think that I would describe any medieval society, let alone governmental system, as unqualified feudalism.