Backspace does not delete a file

Try this: Click anywhere on your Mac's Desktop to open the Finder. Then, use the key combination ⇧ ⌘ N (shift command N) to create a new folder on the Desktop.

Does that work?

Select that folder then ⌘ Delete. That should move that empty folder to the Trash. Does it?

That's a clue. Normally, apps should be installed in your Mac's Applications folder. We could discuss what they're doing on your Desktop, but if you can create and delete files on your Desktop it indicates the ⌘ Delete key chord is working properly and rules out a number of other possible concerns.

In any event apps like Skype and Steam have no business being on a Mac's Desktop. The normal place is /Applications. Use the Finder's Go menu > Applications to open that folder and drag them where they ought to be. You will need to authenticate; that's normal.

Another acceptable place is in your Home folder's Applications folder, which makes those apps available only to you and not all users of that Mac. That's OK too.

No need to drag it then.

Quit Skype first. Can you delete it from the Desktop using any means whatsoever?

If not, restart your Mac in "Safe Mode" and determine if you can delete it while in that mode:

How to use safe mode on your Mac - Apple Support

To learn how to delete items on a Mac, please read Delete files and folders on Mac - Apple Support.