You seem to have installed the X11 version of Zathura. For the version with native macOS integration, follow the instructions beneath OSX_native_integration:
# unlink installed zathura and girara
brew unlink girara
brew unlink zathura
# install HEAD
brew install girara --HEAD
brew install zathura --HEAD
mkdir -p $(brew --prefix zathura)/lib/zathura
ln -s $(brew --prefix zathura-pdf-poppler)/libpdf-poppler.dylib $(brew --prefix zathura)/lib/zathura/libpdf-poppler.dylib
Or, if you haven't installed Zathura yet
brew tap zegervdv/zathura
brew install girara --HEAD
brew install zathura --HEAD
brew install zathura-pdf-poppler
mkdir -p $(brew --prefix zathura)/lib/zathura
ln -s $(brew --prefix zathura-pdf-poppler)/libpdf-poppler.dylib $(brew --prefix zathura)/lib/zathura/libpdf-poppler.dylib