However, as software is everywhere, the original question is the same thing as "what physical invention" is the most important one?
From one standpoint this could be something like the wheel or electrical light, i.e. Bios, compiler or a network stack in the software world. Or, something way more personal, like health care related software for the loved ones or some more profane stuff.
To make the question even less tangible, software in general can be replaced more easily than physical things, most of the time.
The SWIFT Network has no real alternatives and entire countries teeter towards bankruptcies when they're banned from using it.
The last time the US banned Iran, Iran reportedly lost $100M; everyday!
[Edit] Spellings and URL
the successor UEFI im not so happy about but it can be tamed, it seems to be a binary blob thin edge of wedged between the firmware and the OS.