Is Photoshop Elements a Non-Destructive Editor?

There are many editing workflows and some may destroy the original files. You can't imagine an editor which would keep only the original file. Either the editor creates a changed version or it creates a companion file storing the editing process.

So it's very misleading to classify editing softwares as destructive or not, it depends how you are using them. Your workflow may be destructive or not and softwares like Photoshop or Elements can be either destructive or not depending on how you use them.

There is another distinction which is much clearer as suggested above. It's called 'parametric' editing. That's the way Lightroom and all raw convertes work. You store the editing parameters, the sliders values you change in your workflow. The result is a combination of the original file and a small text file storing the editing 'recipe'. That's not so different from creating an action you can apply to an original file. The result is 'virtual', you can create the version when you want.

There, the comparison between Lightroom, Photoshop and Elements shows that all three are tue parametric editors when Photoshop and Elements use the Adobe Camera Raw (ACR) plugin. The main ACR interface is very similar and the editing software engine has the same base. On the other hand, Photoshop and Elements are primarily are mainly 'pixel' editors. That allows a lot more power and flexibility to use layers and detail editing features. You never need to destroy your originals, but you need to create and editing version. With parametric editing, you generally don't need to 'export' a derived version, which saves a lot of disk space.

I never work on the original, only on a copy.

Yes you are correct. It is possible for example to work on a duplicate layer so your original is protected provided you save as a layered document e.g. .psd or .tif

Destructive, like Photoshop.