It very much does exist, and I chose those words on purpose as they're places where the realisation of /h/ is a voiceless palatal fricative (i.e., the German ich-laut) and not a voiceless glottal fricative. "ish" would be a voiceless alveolo-palatal fricative.
I recommend you read up on English phonology, as a video for German learners really isn't a good source.
I recommend you read up on English phonology, as a video for German learners really isn't a good source.