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.
The WILD strategy that they propose is something very different then the way cancer gets addressed normally by big pharma/biotech.
If Larry would think of addressing cancer being part of the aging that he wants to fight I doubt he would have made the argument that it only gives you 3 years of additional life if we would solve cancer.
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".