The new revision of the book is using mdbook, which hasn't yet implemented playground support [1].
An RFC has recently been accepted to start the infrastructure of featuring the new book (and other resources) on doc.rust-lang.org/book, but the implementation isn't done yet. Soon!
I hope the quick link to the rust playground in the sample code stays around.
Also curious, is this supposed to be reflected on Rust Stable at https://doc.rust-lang.org/stable/book/