Some of the README contents in doc/ seems to be misplaced, and I suspect it is an heritage from before QT was merged upstream. Mainly I'm thinking about a few instances of Unpack the files into a directory, and then... (and similarly) and also the entire file doc/README_windows.txt.
There may be reasons for this that I don't know about. However, in my opinion, all instructions related to running an already built version of Bitcoin Core belong on bitcoincore.org only, not duplicated (poorly) in the developer documentation. Except for maybe the last line of the build instructions. The README already links to the releases page, which is nice.
Is this about right? If so, I'd be happy to supply a related PR.