It has to be running on a physical computer because its a user interface software designed to be placed on an operating system.
There is no reason why you can't buy a cheap PC and leave running 24/7 just to run Express invoice as a private cloud server, of course you will need to make sure you have firewall configured and other measures to secure your data.
I personally bought this product because it is THE ONLY MAC INVOICING PRODUCT ON THE MARKET that runs on a local computer rather than in the cloud.