Your source doesn't contradict the fact that women's fertility has a sharper and earlier cliff than men's. It doesn't even use the same age brackets for men and women. It compares men age over 45 against men age under 25, whereas for women the study compared those age > 35 vs age < 25.
Gender does matter though. Men can sire offspring into their 60s, women have marked decline in fertility starting from 32 and hit an absolute wall (menopause) by their fifties.
Men offspring-ing in their 60's and dying 10 years later is perfect way to build a society where kids get to grow up without their fathers when they need them the most