Aging is a word that means different things to different people. Some people think of Botox as an anti-aging treatment.
When it comes to tech people and internet intellectuals Aubrey de Gray defined aging a while ago in a way that doesn't include dealing with Cancer and Heart disease.
Aubrey de Gray basically proposed to tackle aging directly instead of spending so much resources on trying to solve various illnesses.
When Larry Page speaks about aging in the way he does it's reasonable to expect that he uses the word in the way Aubrey de Gray frames the debate.
Aubrey de Grey actually does view fighting cancer as a core part of ending aging. His SENS program has 7 steps, one of which is OncoSENS, which specifically is targeted at eliminating cancer.
Heart disease is also an inevitable consequence of aging (because of cell death weakening the heart) RepleniSENS would address this. GlycoSENS would address other cardiovascular problems like arteriosclerosis.
ETA: To clarify, by "aging" I mean senescence.
Google's announcement, Time magazine rather sensationalist headline.
In any case, it's nice to know that Google set its sights to "challenge ... aging and associated diseases". Apple's Tim Cook:
For too many of our friends and family, life has been cut short or the quality of their life is too often lacking. Art is one of the crazy ones who thinks it doesn’t have to be this way.
One more step towards "world optimization".