Unfortunately I ran into a compile problem with msys2 and mingw-w64. I'll post an issue on github:
gcc -D_WINDOWS -D_WIN32_WINNT=0x0502 -Wno-unused -Wno-write-strings -O1 -fno-math-errno -fschedule-insns2 -fno-strict-aliasing -fno-trapping-math -fwrapv -fno-keep-inline-dllexport -fno-common -mieee-fp -mpc64 -I"../include" -c -o "_kernel.o" -I. -DHAVE_CONFIG_H -D___GAMBITDIR="\"\\\\mingw64\"" -D___SYS_TYPE_CPU="\"x86_64\"" -D___SYS_TYPE_VENDOR="\"w64\"" -D___SYS_TYPE_OS="\"mingw32\"" -D___CONFIGURE_COMMAND="\"./configure '--enable-single-host'"\" -D___OBJ_EXTENSION="\".o\"" -D___EXE_EXTENSION="\".exe\"" -D___BAT_EXTENSION="\".bat\"" -D___PRIMAL _kernel.c -D___LIBRARY
_kernel.c: In function '___H__20___kernel':
_kernel.c:14100:37: error: '___gstate_mem {aka struct ___gstate_mem_struct}' has no member named 'glo_list_head'
___glo_struct *p = ___GSTATE->mem.glo_list_head;
^
make[1]: *** [makefile:164: _kernel.o] Error 1
make[1]: Leaving directory '/home/woodring/gambit/lib'
make: *** [makefile:414: all-recursive] Error 1