"It is not necessary to invoke God to light the blue touch paper and set the universe going." In the forthcoming book, published on 9 September, Hawking says that M-theory, a form of string theory, will achieve this goal: "M-theory is the unified theory Einstein was hoping to find," he theorises.
The term of art for this sort of claim is the 'promissory note'. It's a version of the claim 'some day science will be able to explain [something it cannot currently explain]'. The Guardian article doesn't say anything about why Hawking has decided to repose confidence in this particular version of string theory, so we don't have the means to evaluate his decision. So: the story is that Hawking has decided to place a rather large bet on a version of string theory to, one day, explain the law of gravity and hence complete the explanation of why the universe exists. That idea doesn't have any particularly interesting consequences as regards God's existence or nonexistence. If Hawking is right, however, atheism will someday be able to justify itself scientifically without resorting to promissory notes. Sorry to be so non-inflammatory about this-- I teach this material for a living.