I should note that the article does say that the amount of such cells is “vanishingly small”. But still, enough to possibly have some impact on the person carrying them. Whether this is enough to affect future children is another story, perhaps. Still, I don’t see how it could be so lightly dismissed.
The new findings do not imply that telegony is real. The original question asked (and the belief in telegony) was whether the father of one child has a continuing impact on subsequent children from the same mother but a different father.
E.g., Frank and Mary have a child named Carl. Mary then has a second child named Carla, but Carla’s father is Felix. Telegony implies that somehow Frank also “influences” Carla’s make-up.
The article you linked to merely says that a few of Carl’s cells may be left floating around in Mary’s bloodstream, as well as a few of Carla’s. Some of Mary’s cells may live on in her children, as well.
This does not change the genetics of the situation. Obviously, half of Carl and Carla’s genetic material comes from their (different) fathers, but this does not mean that Mary’s gametes were changed between the times of her pregnancies. In fact, Mary’s ovaries have the same eggs (her genetic contribution) when Carla was born as they did when Carl was born and the same eggs as when Mary herself was born (minus losses to her cycle and the children themselves, of course). Eggs develop in the ovaries from cells that are present at birth, rather than being created during later life as sperm are.
I do not see how a few stray cells floating around could have affected the mother’s eggs.