No, x32 is still long mode (64-bit), it's just an ABI that restricts all memory allocations to 4 gigabytes of address space so that 4-byte pointers can safely be used instead of 8-byte ones. You can get a similar effect by manually mmaping memory into the lower parts of the address space even in a regular 64-bit program (luajit relies on this), but you can't stop malloc, the kernel, other libraries, etc. from using the rest of the address space.
On x86 CPUs since the the 386, you don't need a hack to make 32-bit mode look like a 16-bit mode, you literally can access the full 32-bit registers in 16-bit modes with an operand size prefix.
On x86 CPUs since the the 386, you don't need a hack to make 32-bit mode look like a 16-bit mode, you literally can access the full 32-bit registers in 16-bit modes with an operand size prefix.