I also checked similar manual for AMD and it doesn't seem to mention RSP alignment at all, except that "some calling conventions may require ...".
The CPU doesn't care. It only matters when you call functions which allocate 16B objects on the stack.* This function calls only itself and pushes only 8B words on the stack so it's fine with 8B alignment.
* Some functions generated by C compilers do and they segfault if you call them with wrong alignment. Ask me how I know.
edit:
OK, so I downloaded this code. Results:
as-is: 78111us
push rbp: 73093us
sub rsp,8: 72332us
sub rax,8: 72222us
Seems to be a matter of instruction alignment, nothing to do with the stack.
