I don't think Steve Jobs necessarily is responsible for this, but that he was aware that it was going to happen. If the iPhone had shipped with a poor implementation of Flash, which was all Adobe was capable of delivering, Flash would still eventually die off. Jobs was just aware that it was worth the sacrifice of political capital to do away with Flash, since in a few years it would be a moot feature.
Apple had a big hand in this, Whilst there was plenty of negative sentiment towards flash before the iPhone etc I don't remember too many people talking about killing it.
Indeed many website owners liked having flash content on their site, it is only in the last few years that developers can point to a growing and lucrative demographic or users/devices that can't consume flash content.
