Short answer: yes, it does. People often present variants of this theorem that are a lot weaker than its most powerful version.
Whereas Satterthwaite's version only applies to ordinal voting systems, Gibbard's version applies to all deterministic voting systems, including non-ordinal ones. Combining Gibbard's version and a remark made by Satterthwaite, a complete version of the theorem is: "Every deterministic voting system with at least 3 eligible candidates is either dictatorial or manipulable." Here, I use the phrase eligible candidate to mean that the candidate is actually in the image of the voting system (if three candidates exist but you accept that one of them cannot be elected in any situation, then you can consider the simple majority rule on the other two candidates, which is neither dictatorial nor manipulable).
In fact, this result is only a corollary in Gibbard's paper. The main theorem is incredibly powerful in my opinion and deserves to be known more widely: "Every straightforward game form with at least three possible outcomes is dictatorial." A game form is similar the the usual notion of game, except that you do not provide a priori the preferences of the player over the possible outcomes. For example, matching pennies and battle of the sexes can be viewed as two different games corresponding to the same game form. The word straightforward means that, given your preferences, you always have an undominated strategy. In other words, applied to voting systems, it means that whatever your preferences are, you can choose the ballot that best defends your opinion, without knowing what other voters will do.
To finish with the deterministic framework, I'd like to comment on the case where some voters can be indifferent between two candidates or more. As noticed by Satterthwaite, the original theorem immediately implies that, on the subset of configurations where all voters have strict preferences, the system is dictatorial (given the usual assumptions, i.e. non-manipulability and at least 3 eligible candidates). Which is already not very good...
But you can imagine the following system, called sequential dictatorship. Step 1 : if voter 1 has a most-liked candidate, then this candidate is elected. Otherwise, restrict the possible results to her most-liked candidates. Step 2 : if voter 2 has a most-liked candidate (among the remaining ones), then this candidate is elected. Otherwise, restrict the possible results again. And so on. This system is not manipulable, and it is not dictatorial, in the sense that the result does not depend only on voter 1's ballot.
However, it is dictatorial in Gibbard's sense: for any eligible candidate, voter 1 can cast a ballot such that this candidate is elected, whatever other voters do. So, even if indifference is possible, you cannot really escape Gibbard's theorem...
Manipulation of Voting Schemes: A General Result, Gibbard, 1973.
Strategy-Proofness and Arrow’s Conditions: Existence and Correspondence Theorems for Voting Procedures and Social Welfare Functions, Satterthwaite, 1975.
But there is more: in 1977 and 1978, Gibbard extended this result to non-deterministic voting systems. A voting system is unilateral if the outcome only depends on the strategy (i.e. ballot) of one voter. A voting system is duple if the final outcome is restricted to a pair of alternatives. In short, the theorem goes like this: "Any straightforward game form (deterministic or not) is a probability mixture of game forms each of which is either unilateral or duple."
Intuitively, you can design a non-manipulable voting system like this: you draw a voter at random, and the outcome (which is a probability distribution on the candidates) depends only on her ballot. If the outcome attributes a probability 1 to her most-liked candidate, the system is called a random dictatorship. But other systems are possible: for example, probability 2/3 for her most-liked candidate, and 1/3 for her second most-liked candidate.
You can also design a non-manipulable voting system like this: you draw two candidates at random, and voters choose between these two according to a specific voting rule (for example simple majority).
The idea of the theorem is that any non-manipulable voting system is a probability mixture of these two types. For example, you toss a coin, and then you use the first or the second system.
Now, what happens if you add a very reasonable requirement to your voting system, for example unanimity? This word means that if a candidate is the most liked for all voters, then she should be elected with probability 1. With this additional requirement, the only suitable voting systems are random dictatorships. You draw a voter at random (not necessarily uniformly), and this voter chooses the winner.
Straightforwardness of Game Forms with Lotteries as Outcomes, Gibbard, 1978.