You should use the AMD64 handbook, not the x86 handbook, if you're trying to
install on x86_64 hardware.
https://wiki.gentoo.org/wiki/Handbook:AMD64
More importantly, you should be booted into a 64-bit environment. That means
using a 64-bit live image for your initial boot, and using an amd64 stage3.
EFI has similar requirements; you'll need to be booted via EFI in the first
place in order to set up the bootloader properly; your firmware won't make the
necessary hardware calls available to register your bootloader if you're not
booted in EFI mode.
HTH