The desktop context menu isn’t and never has been modified by the USB version, as far as I know. Doing that requires installing a shell extension on the machine.
Support for Desktop double-click was only recently added to the USB version, and may require you to edit the config file that’s put on the USB drive. It also won’t be enabled until you launch Opus from the USB drive, and leave Opus running in the background. (I think it also only currently works when running the 64-bit version, too. Or maybe only when running the version which matches the bitness of the computer itself. It’s still a somewhat experimental feature for USB mode.)