I am sure SmartBear folks will come back with an official response. But the article you linked in your OP specifically talks about including units from one project to another by adding them as existing items, essentially making them common libraries of code. Nothing is mentioned in that article about what happens if those units are dependent upon a particular UI plugin. Basically, to use something across multiple projects, you need to include it in multiple projects. So, if you have an item that has a dependent on a particular plugin and you are including that item in another project, that other project is now also dependent on that plug in. To make it even simpler... in Project1 if I have Unit1, Unit2, and Unit3 and Unit3 calls functions from Unit1 and Unit2, if I add Unit3 to Project 2, I also need to add Unit1 and Unit2 as well otherwise Unit3 will fail. This is not a matter of plugins, it's a matter of context. Such is the case, really, in any technology.
For example, in Netbeans when I'm developing java applications, if in one application I create a class that is dependent upon having a particular jar included in the project, if I take that class to a different project, I must also include that jar in that project. I can't just expect the class to work in the new project if I don't bring over it's dependencies as well.
That's basically the scenario you created. Your tests and code and such in your first project are dependent upon a particular plug in.... to use them in a different project, you need to bring that plug-in along for the ride. I don't know exactly what the plug in is, who created it, etc... but if you have code dependent upon it, that code will not work if the plug-in is not present.