The Puffin Classics books are/were aimed at the same audience that would read the Target novelizations, anyone from 7 to 70.
I don't know that the Quirk Books comparison is really valid. For one thing, those books retained some (much?) of the original text and warped it to incorporate something from outside the original narrative. The Puffin Classics don't do that. They're original novels in which the Doctors' story intersects with a tale from classic literature.
If I had the opportunity to write
War and Peace and Time or
The Doctor of Zenda (working title, this was the other Puffin Classics idea I was toying with), I wouldn't have been lifting large sections of Leo Tolstoy or Anthony Hope's text. I'd take the settings and the characters, then do something original with it that respected, and maybe added to, the original. (
Zenda would have had timey-wimey shit going on, and that's clearly not in Hope's original.

)
There's a lot one can do with
War and Peace. There are these huge gaps, characters disappear for hundreds of pages, and major historical events get obliquely referenced if at all. And it's a book I have argued with, because it goes places I don't agree with, and it doesn't show the things I want to see. I wanted to play around in those gaps, like 1814, which Tolstoy sums up in like two lines in the First Epilogue but there's big stuff there -- the fall of Paris! -- I want to read about.
One problem I ran into -- and I'm not sure if I needed to solve it -- was that I had absolutely nothing for Natasha to do. She would get
mentioned, but I don't believe she would have ever appeared on page. Other Rostovs would have -- 1814 would largely be from Nikolai's perspective -- but Natasha is such a sheltered character that she doesn't have the space for her story to intersect the Doctor's. Plus, I generally detest Natasha as a character; the adaptations generally tone her down, but she's a
lot on the page.