Interestingly, starting coqtop with two -emacs arguments is actually fine. It seems the debug message printed on newer PG versions is missing some quotes around the program name that it actually tries to run. I assume the actual underlying failure is from trying to run "coqtop -emacs" -emacs, not "coqtop" -emacs -emacs as it is printed.

Thanks for the report! Above the only occurrence of -emacs I read "The default names for proof assistant binaries may work on your system. If not, ..." in Appendix A. Therefore, I would not say the manual instructs people to add -emacs... Did the default names of the binaries not work for you?
I agree that there seems to be a problem with the documentation. Setting coq-prog-name as documented should not raise such an error, even in case the default binaries do work.
Have you customized coq-compile-before-require or do you see this problem with the default setting of nil for this setting?
The latest changes in that part of the manual are from 2000. @Matafou: To me this looks like we forgot to update that part of the manual when we changed the code to add emacs as argument.

Indeed this part of the manual needs update.
AFAIK the good answer is: coq-prog-name should contain the executable name ONLY, with no option or argument, and options should go into the list coq-prog-args (and of course -emacs is useless because added by PG anyway but this is indeed innocuous).
That said even this, while correct, is a bit outdated since writing a _CoqProject is better almost in any circumstances and you don't need to care about these variables anymore.
I will try to fix this part of the documentation. Thanks for reporting.