It doesn't seem like a right on it's own, so much as included in the existing right to "liberty". My 2 cents.
However, it goes further as they found that as per Mathews v. Eldridge, 424 U.S. 319, 333 (1979) the plaintiffs constitutional right to due process has been violated because:
1. not only do they have a right to travel internationally, being placed on the no-fly list stigmatises them as the government discloses the list to other parties (such as ship captains) and additionally deprives them of their liberty.
2. Notice is insufficient as there is inadequate information given to those on the no-fly list, because under government policy they neither confirm nor deny they are on the list. This leads to a catch-22 situation where you cannot appeal an erroneous decision as you cannot tell what that decision was.
Interestingly, the court said they couldn't determine if there were issues with judicial review.
There is a third test, which is to weight the government's interest against issues with disclosure, but this couldn't be determined by the Court.
The ruling is quite readable, btw. It can be found here:
https://www.aclu.org/sites/default/files/assets/latif_v_hold...
Again, not trying to be pedantic, but this is another major point of contention in Constitutional law - how broad of a scope do each of the Constitutional named rights have? The 9th Amendment implies that it is extremely broad, as it explicitly reserves non-enumerated rights as falling under the Constitution.
DISCLAIMER: just to head things off, I bring up Roe v. Wade not because of the topic of the case, but because the general opinion on the ruling's use of the 9th Amendment is pretty consistent (and there are numerous subsequent cases that deal almost solely with this). There are many who agree with the outcome but have major reservations with the potential repercussions of the legal reasoning.
However, you can just look at the general consensus on Roe v. Wade to see that it's far from universally accepted that the 9th Amendment is that broad (that the crux of the opinion is very flawed, relying on a very strange and far reaching right of privacy derived from the 14th Amendment and 9th Amendment - neither of which mention privacy. To clarify - on both sides of the Roe v. Wade debate, most will admit the ruling was flawed, and when relying on it as precedent, nearly all judges will also refer to subsequent cases that address the problems with that ruling). So, the Constitution does not guarantee a right to travel (and the way this ruling is phrased suggests that an appeal would bring this as a concern, and in upholding the ruling, a higher court would almost certainly clarify this). A more likely argument (in terms of its strength in Constitutional law) is one that protects a right to travel as a part of the 1st Amendment right to free speech, expression, and assembly (so a negative right granting freedom from unlawful interference in travel by the government).
To this the Court has found that there was no due process, therefore the no-fly list - as it stands now - violates the United States Constitution.
The right to travel, in the broad sense of "you have the right to move wherever you want to move so long as no laws are violated," is likely covered by an umbrella of the 1st Amendment right to free speech and expression, as well as the 9th Amendment, as a negative right: you are free from being prevented from travel by means not permissible by law or Constitutionally.
However, if the decision relies on other grounds (either solely or in addition to), then I doubt it is overturned. While the Reuters article presents this as legally binding, if the quotes occurred in dicta (discussion of the facts and implications of the case that are not legally binding, as they are not grounded in case or black letter law), then it's not binding, and the ruling can be upheld without addressing the redefinition of liberty.
https://www.aclu.org/sites/default/files/assets/latif_v_hold...
I summarised the case in this comment:
Why not?