In most Unix variants, programs are always installed "silently". Most Linux distributions and BSD descendants have a "package manager" program, which takes care of installation by just extracting all files from a package to standard locations, without asking anything. (One exception is Debian with its post-installation
debconf, but it too can be skipped.)
But Cygwin is not "Linux world". It is just an emulation layer of certain Unix (not Linux
*) features, along with a collection of popular Unix programs compiled to run on that emulation layer.
setup.exe is not "Linux world" either. It is a pure Windows program - an installer - and a very poor one, at that.
(Every other installer tool for Windows does have a silent mode, although its activation varies;
/silent switches are common.)
* Linux is one Unix-like operating system out of many. There is *BSD, Mac OS X, Solaris, Hurd... While Cygwin may be considered an Unix environment, I certainly would not call it "Linux".