[Casimiro Notevi]

También puedes hacer todo sin ensamblador, ejemplo:

Código Delphi [-]
unit Unit4;

interface

uses
  Windows, Messages, SysUtils, Variants, Classes, Graphics, Controls, Forms,
  Dialogs, StdCtrls;

const
  PROCESSOR_ARCHITECTURE_AMD64 = 9;
  {$EXTERNALSYM PROCESSOR_ARCHITECTURE_AMD64}
  PROCESSOR_ARCHITECTURE_IA64 = 6;
  {$EXTERNALSYM PROCESSOR_ARCHITECTURE_IA64}

type
  TForm4 = class(TForm)
    bt1: TButton;
    procedure bt1Click(Sender: TObject);
  private
    { Private declarations }
  public
    { Public declarations }
  end;

var
  Form4: TForm4;

implementation

{$R *.dfm}

function GetNativeSystemInfo(var SystemInfo: TSystemInfo): Boolean;
type
  TGetNativeSystemInfo = procedure (var SystemInfo: TSystemInfo); stdcall;
var
  LibraryHandle: HMODULE;
  _GetNativeSystemInfo: TGetNativeSystemInfo;
begin
  Result := False;
  LibraryHandle := GetModuleHandle(kernel32);
  //
  if LibraryHandle <> 0 then
  begin
    _GetNativeSystemInfo := GetProcAddress(LibraryHandle, 'GetNativeSystemInfo');
    if Assigned(_GetNativeSystemInfo) then
    begin
      _GetNativeSystemInfo(SystemInfo);
      Result := True;
    end
    else
      GetSystemInfo(SystemInfo);
  end
  else
    GetSystemInfo(SystemInfo);
end;

function IsWindows64: Boolean;
var
  ASystemInfo: TSystemInfo;
begin
  GetNativeSystemInfo(ASystemInfo);
  Result := ASystemInfo.wProcessorArchitecture in
                    [PROCESSOR_ARCHITECTURE_IA64, PROCESSOR_ARCHITECTURE_AMD64];
end;


procedure TForm4.bt1Click(Sender: TObject);
begin
  if IsWindows64 then
    ShowMessage('Es 64 bits')
  else
    ShowMessage('Es 32 bits');
end;

end.