According to https://stackoverflow.com/questions/49148568/api-ms-win-core-dlls-missing-on-windows-10#comment85301714_49148568 :
You mean you ran
depends.exe? It’s quite old and doesn’t support API sets, try github.com/lucasg/Dependencies
windows - How to check for DLL dependency? - Stack Overflow also suggests dumpbin (doesn’t check for DLL presence) and ldd (present in Travis as part of Git Bash environment).
See Linking against ncurses, no package from Chocolately yet - Environments / Windows - Travis CI Community for what is available on a Travis Windows builder.