There is usually no need — and probably a bad idea — to set PATH to a literal value in ~/.zshrc . You can also delete some directories that were previously added to PATH .
In your case, when it worked with a different shell, I would first try to simply delete the line where you set PATH , since zsh should inherit PATH from its own parent environment.
If this does not add the path containing gulp (possibly because it was previously added to the configuration of your old shell), you can add
PATH=$HOME/.node/bin:$PATH
to your ~/.zshrc .
Note: since PATH already part of the environment, there is no need to export it again.
Typically, if you want to add something to your PATH , you can use:
PATH="/something/new/bin:$PATH"
This adds /something/new/bin to PATH
If you really want to remove something from PATH , this should do the trick:
PATH=${${PATH//\/something\/old\/bin/}//::/:}
This removes any occurrences of /something/old/bin (slashes must be escaped) from PATH , and then removes duplicate colons.