Of course, the Angelica Bell bits of Shadow Play aren't really 'continuity' although they are portrayed as such. They're part of the Look and Read programme as part of the classic 'bit in the middle' device within the story, reimagined for the 21st century. Clearly they decided to use the CBBC continuity style as a fake 'linking between programmes' idiom to shoehorn the 'bit in the middle' around the story. Not a bad choice, given how kids would have been used to that style of CBBC continuity in 2004.
Interesting BBC logo in the lower-third of the opening, too...!
It was only at the time of the CBBC revamp in September 2007 that all presentation, including the DOG, was removed from Class TV, with each programme followed directly by the next. By this time it had been reduced to a 75 minute slot around lunchtime, and of course disappeared altogether the following spring.
Indeed, that's visible at the end of the second video, which has clearly come from that era of Class TV, as it goes straight from the Look and Read endcap into the Watch titles.