You should create an installer that always runs dxwebsetup.exe, in case it is needed.
Google Chrome (and presumably other browsers) have an agreement with Microsoft that allows them to ship certain DirectX files with the browser to use hardware acceleration. However for legal reasons unless you have your own agreement with Microsoft you cannot ship these DirectX files with your game, except for the dxwebsetup.exe installer (which has the correct EULA agreement and so on). If the DirectX files are missing, node-webkit will not be able to use hardware acceleration. If the user happens to have them installed already (e.g. another game installed dxwebsetup.exe), it will work out of the box, but you can't rely on that being the case.
IMO it's another good reason to go with web publishing: no need to worry about installers, security prompts, waiting for downloads etc - just runs right away from the URL.