The file:

/usr/include/machine/_types.h

reads:

typedef long __int64_t;
typedef unsigned long __uint64_t;

This causes types int64_t and uint64_t be of width 32 when being compiled in the 32-bit mode.

Fix: 

These definitions:

typedef long __int64_t;
typedef unsigned long __uint64_t;

should be replaced with something like:

#if defined(__LP64__)
typedef long __int64_t;
typedef unsigned long __uint64_t;
#else
typedef long long __int64_t;
typedef unsigned long long __uint64_t;
#endif
How-To-Repeat: $ cat x.c
#include <stdio.h>
#include <stdint.h>

int main(void)
{
    printf("%d\n", sizeof(uint64_t));
    return 0;
}
$ gcc -m32 -B/usr/lib32 x.c
$ ./a.out
4