The key part is at the very end
It might be possible that the advantage of receiving long telomeres from an old father is more than offset by the disadvantage of higher levels of general DNA damage and mutations in sperm, he said.
According to the BBC all they've done is show that older men have longer telomeres [though as BH says unclear exactly who they mean by 'older men']. On the basis that longer telomeres may predict longer life expectancy, they believe it is possible older fathers will have children who will live longer.
But it's all very hypothetical... there is no actual evidence for such a conclusion. Given that it is known that DNA in sperm is increasingly damaged with time, it is equally possible that children of older fathers are more likely to suffer from various genetic diseases. The risk of miscarriage increases. So perhaps overall life expectancy would not be increased and even if it were, would it out-weigh the extra suffering?