For what it's worth, the word "electronic" in that description is a lot more load-bearing than it looks, excluding machines such as the Harvard Mark I (ASCC) and Bell Labs Relay Computers, both of which were solving problems under program control years earlier (unlike the Eniac, which initially had to be rewired for every problem -- stored-program control was added years later).
I highly recommend the book "ENIAC in Action" for a thorough discussion of the computer.
Personally, I view ENIAC as the first influential computer, in the sense that it made multiple groups decide to build computers and thus started the computer revolution. If you went back in time and stopped ENIAC, it would have set back computing by years; the impact of earlier computers was small.