Even if you go from the launch date and not the last errata, the i586 architecture is only 28 years old. In today's world of copyright, that's practically an infant.
To be clear of most patents, you generally need at least thirty years, and copyrights are generally more than twice that number.
You will probably require a license from Intel. (Though whether or not they care enough to enforce things is another matter entirely).
From what I recall, the closest thing to an answer I've received in the past is that you can not use the manuals to a modern x86 chip (or other part) to learn the instruction set. The use of any copyrighted material infects you project if the rights holder is particularly egregious about enforcement to that level.
It's the same thing with the IBM PC BIOS reverse engineering. If you'd seen the BIOS manual, you couldn't work on the clone. I can't recall if that was purely seeing it or because the source code to the IBM BIOS was printed in the back of the manual.
I know Intel, Microchip, and ARM have aggressively shut down any FPGA project that implements an instruction-level compatible core of x86, AVR, PIC, or ARM CPU. Intel seemingly hasn't gone after any of the 16-bit x86 core implementation, but I haven't seen an open source 386 or newer core.