Why would males' shorter pension's savings produce more, and not less, income?
I suspect your confusion is merely because you don't know what an annuity is. An annuity pays you a regular stream of income until your death (e.g. $10,000 every year until you die).

So say there's a man and a woman. Each is aged 65 and each has \$100,000 in pension savings. Each person uses their pension savings to buy an annuity.

Suppose the financial institution (usually an insurance company) selling them the annuity estimates that the man's life expectancy is 20 years, while the woman's is 40 years. Then the actuarially-fair payout would be \$5,000 per year for the man and \$2,500 per year for the woman (if we ignore interest rates, discount rates, and similar complications).

Hence, for the same amount spent on the annuity (\$100,000), the man gets a highly yearly income (\$5,000 per year) than the woman (\$2,500 per year). This is what your quoted passage means.



(More on how the annuity works: If the man/woman lives longer than the expected 20/40 years, then good for him/her. He/she keeps receiving the agreed-upon yearly payout even past those 20/40 years. 

Conversely, if the man/woman lives shorter than the expected 20/40 years, then too bad for him/her. He/she gets the agreed-upon yearly payout only until he/she dies.)