MacUpdate Desktop doesn't require any further uninstallation steps aside from being moved to the trash. If you are unable to empty your trash, you may still need to quit all MacUpdate Desktop processes. Do this by clicking the MacUpdate Desktop menu item, then clicking the gears icon and selecting Quit MacUpdate Desktop:
After doing this, you should be able to empty your trash.
If you don't see a MacUpdate Desktop menu item or it's unresponsive, you can force quit the app from the Force Quite Applications dialogue by pressing ⌘⌥Esc (Command + Option + Escape) and quitting MacUpdate Desktop, or launching Activity Monitor and quitting any MacUpdate Desktop processes. By ensuring you've quit MacUpdate Desktop, you'll be able to empty your trash and remove MacUpdate Desktop.