The GVS changed the quality of ME long vowels, but the perception of length persisted in some dialects by diphthongizing the moved (now tense) "long" vowels, now phonemic tense /i, e, o, u/, resulting in [iy, ey, ow, uw] as normal allophones of the tense vowels.
[w] is the labializing offglide for tense rounded vowels /o/ and /u/ (also for back vowels, because English back vowels are rounded, whereas front vowels aren't); and [y] is the palatalizing offglide for tense front vowels /e/ and /i/. These offglides affect what comes after the vowels.
This can be perceived easily by observing the behavior of tense vowels before resonants, especially /l/ (/r/ has other issues after vowels). Many English speakers use an epenthetic schwa in words like fool, feel, foal, fail.
I.e, in these words, for these speakers, there are two syllables -- the first stressed onesyllable with a tense vowel -- and the second, short syllable, consisting of a reduced vowel ([ə] or [ɨ]) and the final /l/. In essence, a syllabic resonant.
Indeed, the phenomenon of tense vowel diphthongs is one of the major features of an English accent in other languages. Any native English speaker who can learn to say pure tense vowels [i:, e:, o:, u:] at normal speech rates, without diphthongizing their vowels, can improve their accent greatly in any European language, for instance, because none of them have this feature, but rather use pure vowels throughout, except for phonemic diphthongs like /ay/ and /oy/. And /ow/ and /ey/ are likely to occur and be phonemically distinct from /o/ and /e/ in those languages, anyway.