execinfo.h missing when installing xgboost in Cygwin
You can put #undef DMLC_LOG_STACK_TRACE right after it's definition on line 45 here. See example in this gist.
execinfo.h is only available on Linux, but in this project it is used only for debugging and printing stack trace on Linux. There is a check for Mingw in their codebase, don't know why it is not defined (they've disabled it, see this PR).
You should try to change those lines and run make again.