Whatever it is they are "moving through" is not necessarily a part of, or independent of, the location they are going to. This can't reliably be used to determine the nature of the realm they are going to.
Actually yes it can. Here is the sentence:
"the Sailor Warriors moved through that dimensional space, going to a world beyond this three-dimensional realm"
For simplicity sake:
Let A be "that dimensional space"
Let B be "a world"
Let C be "this three dimensional realm.
The sentences uses 'that" for A, and 'this' for C. This means A and C are separate locations. (ex that dog and this dog are two different dogs, That city and this city are two different cities, that person and this person are two different persons etc.)
C is by virtue of being a three dimensional realm is also a dimensional space.
A and C are both separate locations and also are dimensional spaces.
A dimensional space beyond three-dimensional realm must have a different dimensionality than the three-dimensional realm. It can't be 0,1 or two, or the cast couldn't exist in it.
Here are the possibilities:
(B and C are inside A) or (B and C are not inside A)
Conclusion 1: If B and C are inside A, then B is a dimensional space just like C and A.
If B and C are not inside A then,
Conclusion 2: A is a dimensional space that is connecting C, a dimensional space, to B, a dimensional space.
Conclusion 3: A is a dimensional space that is connecting C, a dimensional space to B, a non-dimensional space.
Two out of three logical conclusions say that B is dimensional space.
But it's not done. Because A and C are both dimensional spaces and A and C are also different, A is not part of the three-dimensional realm either.
If Conclusion 1 is correct, then B is a higher dimension than C, because it is beyond the three-dimensional realm. A is also a higher dimensional than both B and C to contain them both.
If Conclusion 2 is correct, then B is higher dimension than C, because it is beyond the three-dimensional realm. A is also higher dimensional than C but there is no way to know if it has higher dimensionality than B.
If Conclusion 3 is correct, then B doesn't have dimensionality and can be disregarded, but A still has dimensionality, and is still not apart of the three-dimensional realm so it must have a different dimensionality than C.
So either way you slice or dice, there is at least a 4 dimensional space involved here.