What you are doing by including files is called SSI, server side includes. Normally files which use SSI have an *.shtml extension but sometimes an *.html extension is supported as well.

SSI, as its name suggests, is performed server-side. Therefore, the server hosting the files needs to support it. Apparently the remote hosts you are using support SSI but your local computer does not, and therefore it won't work locally. That's okay - just upload the files and it should all work.

It's similar to how a web dev language such as PHP operates. You can't execute PHP code locally without installing Apache or the like on your home machine.

If you wish to be able to test SSI out locally, install the Apache server (windows version) on your home machine. Otherwise, create a folder no one knows about on your remote host to do testing