CONFIG_X86_64 is not available for the selected architecture x86.
Result is shown for architecture x86 or 64BIT

CONFIG_X86_64 (not configurable)

modulename: gdt_idt.ko

and/or

sys_x86_64.ko

and/or

vdso-image-64.ko

and/or

hv_apic.ko

configname: CONFIG_X86_64

Linux Kernel Configuration
└─>X86_64
In linux kernel since version 2.6.12 )
source code:
arch/x86/boot/startup/
selects
CONFIG_ARCH_HAS_GIGANTIC_PAGE
CONFIG_ARCH_SUPPORTS_MSEAL_SYSTEM_MAPPINGS
CONFIG_ARCH_SUPPORTS_INT128
CONFIG_ARCH_SUPPORTS_PER_VMA_LOCK
CONFIG_ARCH_SUPPORTS_HUGE_PFNMAP
CONFIG_HAVE_ARCH_SOFT_DIRTY
CONFIG_MODULES_USE_ELF_RELA
CONFIG_NEED_DMA_MAP_STATE
CONFIG_SWIOTLB
CONFIG_ARCH_HAS_ELFCORE_COMPAT
CONFIG_ZONE_DMA32
CONFIG_EXECMEM
CONFIG_ACPI_MRRM

depends
CONFIG_64BIT