Just to clarify: you are using MinGW in a Cygwin environment and "cross-compile" to native(/MinGW) Windows?
I have not used cygwin in years, and this particular setup is thus untested for libopenmpt. It should work though.
Which GCC is MinGW using? Which MinGW/msys variant (mingw32 or mingw-w64)?
Anyway, I'll assume MinGW-w64 with what looks like GCC version >= 8.1 for now, which means that configure will enable -std=c++17, which in turn makes mptAlloc.cpp expect working C++17, which GCC/libstdc++ fail to provide on MinGW.
Can you please try the attached patch (and avoid export CXXFLAGS="-std=gnu++11")?
Sorry for the delayed answer. OpenMPT team was busy at Revision demoparty.