Here is what configure detects:

configure:27264: Checking libraries for plugins in sys/
configure:27268: checking for X
configure:27376: gcc -E -I/mingw/include conftest.c
configure:27376: $? = 0
configure:27407: gcc -std=gnu99 -o conftest.exe -g -O2 -I/mingw/include  conftest.c -lX11  >&5
conftest.c: In function 'main':
conftest.c:78:1: warning: implicit declaration of function 'XrmInitialize' [-Wimplicit-function-declaration]
 XrmInitialize ()
 ^
f:/e28/mingw/bin/../lib/gcc/i686-w64-mingw32/4.9.0/../../../../i686-w64-mingw32/bin/ld.exe: cannot find -lX11
collect2.exe: error: ld returned 1 exit status
configure:27407: $? = 1
[snip]
configure:27446: result: no
configure:27462: *** checking feature: X libraries and plugins ***
configure:27466: *** for plug-ins: ximagesink ***
configure:28003: checking for X11/Xlib.h
configure:28003: gcc -std=gnu99 -c -g -O2  -I/mingw/include  conftest.c >&5
configure:28003: $? = 0
configure:28003: result: yes
configure:28037: *** These plugins will be built: ximagesink

This enables ximagesink, which fails to build later on:

make[3]: Entering directory '/src/mingw/gst-plugins-base-1.0-1.3.1-1/bld/sys/ximage'
  CC       libgstximagesink_la-ximagesink.lo
  CC       libgstximagesink_la-ximage.lo
  CC       libgstximagesink_la-ximagepool.lo
../../../gst-plugins-base-1.3.1/sys/ximage/ximagesink.c:119:24: fatal error: X11/XKBlib.h: No such file or directory
 #include <X11/XKBlib.h>
                        ^
compilation terminated.
../../../gst-plugins-base-1.3.1/sys/ximage/ximagepool.c: In function 'gst_ximagesink_handle_xerror':
../../../gst-plugins-base-1.3.1/sys/ximage/ximagepool.c:57:3: error: implicit declaration of function 'XGetErrorText' [-Werror=implicit-function-declaration]
   XGetErrorText (display, xevent->error_code, error_msg, 1024);
   ^
../../../gst-plugins-base-1.3.1/sys/ximage/ximagepool.c:57:3: error: nested extern declaration of 'XGetErrorText' [-Werror=nested-externs]
Makefile:641: recipe for target 'libgstximagesink_la-ximagesink.lo' failed