Hmm, well, when I checked the books I have to hand it seems that the ones that have a story within each chapter (more or less, they also tend to have a thread running through but in a less obvious way than a novel plot with a clear beginning, middle and end) are also veeeeeeeeeery old! For eg, Beezus and Ramona (Beverly Cleary), The Magic Faraway Tree (Enid Blyton), Milly Molly Mandy (Joyce Lankester Brisley - published in 1928!!!). Clementine by Sara Pennpacker is the only more recent one I could find on my shelf that was similar in that way. I'm thinking Goonie Bird Green felt a bit like this to me too - that you could quite happily put the book down after a chapter (not that that meant you wouldn't pick it up again, just that there wasn't the same cliffhanger-style 'will they succeed?' type plot thread running through it).
I dunno, maybe I'm just reading too much into my reading, ha! I thought I'd read somewhere that chapter books were like this, to avoid readers giving up on the story, but maybe what I read was about early readers.