Sorry, I have missed your screenshot. From that screenshot, I assume that is from all program menu, which is linked to your installed application. And on your desktop that one is a shortcut icons to the installed application. For those on your Start10 "All Program", all program that you installed will be listed there. I don't think you can delete it there. But you can delete those shortcut icons.
Also you might need to turn off the "Default to the all programs list on menu open" as show below. And only show those icons you want instead.
Stardock Community Assistant