Story

And the story right above this one is that telegony, roundly denounced by prevailing scientific wisdom for over a century, may actually be true.

Extraordinary claims require extraordinary evidence. I am very skeptical with this one. Not my field of expertise, so what I do here is nothing more as speculation. However, I suppose some scientific papers have been misinterpreted and/or to much dumbed down by journalists. Would not be the first time.

Various non-genetic inheritance mechanisms make it possible for environmental factors to influence characteristics of a child.

Sure, changes through the environment may make children stronger, weaker, taller, smaller, may influence the immune system. No doubt about that. Question is what is meant with 'resemble'? In a human context it would mean something like hair colour, eye colour, facial features...the usual stuff when people say 'this kid resembles his mother/father/grand parents, etc. But those traits are encoded in DNA. I don't see a way how these traits can be passed without DNA just by some chemicals in the males sperm. Not saying this is impossible. And maybe there is DNA involved in some unknown way. However... as I initially said: Extraordinary claims require extraordinary evidence.