Nice patch :-)

I think the two function approach works well.

Since you have already checked that termsize is not NULL, Py_DECREF can be used instead of Py_CLEAR.

Would it not be better to use sys.__stdout__ instead of 1 in the documentation and to use STDOUT_FILENO instead of 1 in the code?

A brief google suggested that Solaris requires sys/termios.h for TIOCGWINSZ. Perhaps also only define TERMSIZE_USE_IOCTL if TIOCGWINSZ is defined.
Like so:
#if defined(HAVE_SYS_IOCTL_H)
#include <sys/ioctl.h>
#if defined(TIOCGWINSZ)
#define TERMSIZE_USE_IOCTL
#else
#define TERMSIZE_USE_NOTIMPLEMENTED
#endif
#elif defined(HAVE_CONIO_H)
#include <windows.h>
#include <conio.h>
#define TERMSIZE_USE_CONIO
#else
#define TERMSIZE_USE_NOTIMPLEMENTED
#endif

(didn't check the windows parts)