Making a Storyline so users can click on it as a desktop icon and open from there?

A published Storyline course is launched from one file (e.g., a story.html file on the web or the index.html file in an LMS). That one file accesses lots of other files to play the course. Depending on the size of the course and the assets used, those files could take up a lot of space.

Storyline doesn't include a way to put all that into a "tool" that would launch and play from someone's desktop. 

If the course is available on a website (that is, somewhere outside the LMS), you could give folks a link to launch it.

I haven't ever used it but isn't Reach 360 another solution for what your boss is trying to accomplish? according to Articulate, it's a "quick, frictionless way to deploy training, especially when they need to reach external audiences or want to avoid traditional LMS complexities.

I'll echo what the others mentioned about hosting a web-export and having people access it through a hyperlink on the desktop. One of the downsides to standalone tools is people often still hang onto them even after they've become outdated. Hosting a Storyline-built tool on the web (e.g., a company's shared drive) and having people access it there makes it much easier to update, and everyone is only ever accessing the most up-to-date version.

Storyline used to have an option that created an .exe, called publish to CD, but that was deprecated a while back, perhaps for security reasons. If you all really need a standalone executable, you'll need to publish to Web, and then run it through Electron. It's essentially a standalone browser that only runs your published course.