react-native-desktop depends on cross-platform development tools, so prerequisites are pretty similar for all supported platforms. In nutshell, toolchain is the same as for original react-native + native dev tools (Qt framework) + build system based on cmake.
Recommended way to install required tools and libs is to use Chocolatey package manager.
choco install -y nodejs.install python2 cmake git
Download and run Qt 5.12.2 installer for Windows. During installation process on Select Components screen check Qt 5.12.2 / MinGW 5.3.0 32 bit, Qt 5.12.2 / Qt WebEngine and Tools / MinGW 5.3.0 components. Finish installation process.
Recommended way to install required tools and libs is to use Homebrew package manager.
brew install node watchman cmake
Download and run Qt 5.12.2 installer for Mac OS. During installation process on Select Components screen check Qt 5.12.2 / macOS and Qt 5.12.2 / Qt WebEngine components. Finish installation process.
sudo apt-get install -y git cmake nodejs-legacy npm gnome-terminal
Download and run Qt 5.12.2 installer for Linux. Finish installation process.
sudo dnf install -y nodejs npm cmake git qt5-devel gnome-terminal
Make sure that installed Qt's qmake tool is available in your PATH.
On mac and linux you can add following to .bash_profile:
export PATH=$PATH:/Users/MyUser/Qt/5.12.2/COMPILER_NAME/bin