Hi,
When WordPress is installing, de-installing or updating plugins, it's just moving around files in wp-content/plugins. When it updates a plugin, it downloads the new plugin zip, unzips it, moves the old directory (in this case wp-content/plugins/updraftplus) out of the way, and moves the new one in.
If something goes wrong when it does that, all you need to do is give it some help by hand. i.e. Use FTP to go into your wp-content/plugins folder, and remove the existing "updraftplus" directory (which sounds like it is currently half-removed, but not properly). Then you should be able to try installing again from the dashboard.
Best wishes,
David