The general term for this is non-functional harmony. The term's meaning is fairly obvious if you understand the antonym: It means that the harmony does not readily (or usefully, if you prefer) match with functional harmonic descriptors, like "dominant", that are based more or less on the roles that chords play in diatonic scales or those that highly resemble diatonic scales, like the harmonic and melodic minor.
Truthfully, you are going to have a hard time finding a satisfying answer to your question as stated, because tonality outside of diatonic systems (non-functional harmony) is much more difficult to define than tonality within it, and oftentimes you're going to have to look into the theory of the idiom you're analyzing to find a sufficient answer to this question. The major pentatonic scale is a great example of this, and you touched on the problem: What use is there calling the fifth the dominant interval when you can't even form a dominant chord on it? The fact is that you can't really create a strong cadence out of the major pentatonic scale because there's no tritone and no leading tone to the root, so you have to come up with different ways to describe the relationship between notes and chords formed out of the pentatonic scale than T-S-D. What functional tonality does tell you about the pentatonic scale is, as I mentioned above, that with those combination of notes you'll be unable to reproduce a perfect cadence and that therefore you can't create any strong tension-resolve contrasts like you can in the major scale (and other scales that can replicate the V7-I relationship). It is more complicated to do this kind of analysis with the whole tone scale because its relationship to diatonic harmony is considerably more complex, but it is possible. For example, using the whole tone scale built a semitone away from the root gives a collection of notes that strongly suggest the dominant (since you can form V7#5 with them, as well as its tritone sub if you're a jazz person).
To say that this is a deep rabbit hole is an understatement. For example, you can look at twelve-tone as being a total rejection of functional harmony specifically because it is impossible to ascertain any tonality from twelve pitches given roughly equal emphasis. There's also the diminished scale, which reveals a number of connections between chords that are otherwise very difficult to explain within the bounds of functional harmony.