This means that in principle they are transcribed using only the sounds of German and ignoring distinctions that are not made in German. In particular, the English TRAP and DRESS vowels are both mapped onto German ɛ. The STRUT vowel is mapped onto a. Final obstruents are devoiced.
So we have for example
Camden engl. kˈɛmdn̩
Countrymusic engl. kˈantʁ̥iːmʝˌuːzɪk
Flathead engl. flˈɛthɛt
The NURSE vowel is mapped onto œːɐ, and English w onto v.
Wordsworth engl. vˈœːɐtsv̥œːɐθ
World Wide Web engl. vˌœːɐlt v̥aɛt v̥ˈɛp
(I think “aɛ” must be a misprint for “aɛ̯”.)
The authors are well aware that this is not how the words are pronounced in English. In the foreword (p. 138) they compare the English version of Buckingham Palace, bˌʌkɪŋəm pˈæləs, with the germanized bˈakɪŋəm pˌɛləs (and similarly with several other examples).
But mapping onto native German sounds does not always apply. The dental fricatives, θ and ð, we read,
…kommen im Deutschen nicht vor und werden häufig als [s] bzw. [z] realisiert. Diese werden als Substandard eingestuft und in der Transkription nicht berücksichtigt… …are not found in German and are frequently realized as [s] and [z] respectively. These are categorized as substandard and ignored in the transcription…So for example Southampton is germanized not as zaɔ̯sˈɛmptn̩, but as saɔ̯θˈɛmptn̩. See also Wordsworth above.
Sometimes the label “engl.” really seems to be of etymological relevance only.
Happyend engl. hɛpiː ˈˀɛnt
Leasing engl. lˈiːzɪŋ
(In native English, of course, we say ‘happy ending’, while leasing always has a voiceless s.)