First of all, you would have to agree that it is good; and not everybody would agree. There is undoubtedly an element of kitsch about the Swingle Singers, about what they are trying to do, and about how they actually do it.
Yet for me, as for Glenn Gould; work it does.
Now; the more typical successful Swingle arrangement is a contrapuntal piece - like a fugue; but with this particular soprano (Christine Legrand) they sometimes went in for a sinuous melody supported by simple, homophonic, block chords.
The reason this worked is that - as with all the best musicians - Legrand phrases with great, unteachable, uncopyable lyricism - and can sustain this phrasing through the long-line of the melody.
Of course she also has a sweet tone, very large range, nimble technique, and perfect intonation (tuning); but so do lots of other singers.
Her singing of Ward Swingle's melodic decorations (he was the group's founder, arranger, and lead tenor) is simply gorgeous.
But what she has that is special; is this gift (and it is a gift) of lyrical phrasing of the melody.
Note: This is a transcription of the Swingle's version of the Gmin Fugue from Bach's Art of Fugue; also featured in the above link.