Stew just has unusual prosody and a couple of regional vowel pronunciations, and it’s not really that he’s slurring his words (at least in his mind or mine). Things just don’t fall together with the rhythm that most foreign learners or native speakers would expect. Notice that the American man has a moment or two of that also.
However, because Stew’s pronunciation is so different from the General American or RP usually used in textbook recordings, his speech could be confusing to foreign learners if there’s nothing to read along with. So much for the frequent claim of students with bad listening comprehension that “British English” is easier to understand.
Stew’s recording reminds me of a podcast I found for learning Spanish. My reaction upon first listening to the speaker was, “I can’t understand WHAT the hell this woman is saying!” Listening to her while reading the transcript made me realize she was Argentinean, and I decided to pay for a subscription to the podcast so that I could get all the materials and really learn to understand that accent. However, it wasn’t two months before the management yanked that lady and replaced her with two crystal-clear Mexican speakers. The whole thing lost its advantage for me!
It’s interesting to notice that the two Americans have pronunciation that displays what is called the Northern Cities Vowel Shift. It is most noticeable when they pronounce [æ] as [iə], so cat would be something like [kiət]. This is very common, but it’s not standard broadcast pronunciation.