` (back tick) works the same in /bin/sh as it does in Perl (roughly). It doesn't do anything useful in Win32 default shells.
He's trying to set $BLIB_BASE to be the basename of $INST_BIN. Since INST_BIN is a directory, you could likely just use BLIB_BASE=$(INST_BIN)/.. instead.
Otherwise you could change sub postamble to look up the value of INST_BIN at the time the makefile is written and have the Perl code inside of sub postamble compute the basename of that and just output BLIB_BASE=$base instead of trying to get Perl to write a makefile that get a shell to run a command that runs perl that outputs a value to be stored in a variable of the makefile.