In this instance the "left to me" phrase simply means this is what he is now working on, not that he is the only one to fix dumb ol' Turing's mistakes. And he mentioned exactly how Turing "got distracted" in the next question: Turing jumped from project to project. This was something Wolfram described as a sometimes enviable trait. He's not disparaging the guy.
Every single time I read the comments in a post about Wolfram, there is always some nitpicking going on, on words and phrases that don't mean anything special, being blow out of proportion.
I don't know where all this resentment is coming from for this man, but I guess some people just see what they believe, as opposed to believing what they see... Or I've just missed something completely.
His work is brilliant and insightful -- just treat it as work on its own merits and try not to think too much about the sanctimonious tone behind it.
If you handed his writing to a 3rd grader, they'd probably infer that actual research ground to a halt after the scientific revolution until, praise the Lord, A New Kind of Science was published. This seminal work broke all barriers and unified every single field of science through an elegant framework that had escaped mankind for hundreds of years. And, how was this great breakthrough possible, you ask? Well, it was only possible due to the amazing effort behind that other great work, Mathematica. And now, thanks to the breakthroughs of A New Kind of Science, the world is finally able to see the pinnacle of human achievement and computation: Wolfram|Alpha.
When he writes about historical progress of science and engineering, Wolfram peppers his points with citations to A New Kind of Science over and over again while not linking to, say, any other publication, ever. It's beyond egotistical, it's bizarre.
That's interesting because the man himself believes he comes across as egotistical:
"That’s somewhat egotistical because I can say, ‘this would not have happened without me.’"