I don't think there's a good discussion to be had about this article. The referenced paper is based on two data sources. One is a longitudinal study (great!) of "hundreds" of children in one region (not bad!) and only checks parenthood at the rather young age of 23-24 (uhhh). The other study is based on Mechanical Turk questions. In both the article and the fullest version of the paper I can find online [1], no further details are provided -- not the size of the effects, not the statistical power, nothing.
Yeah, checking at such a young age is a serious distortion of the data. The average age at first pregnancy is somewhere around 30. That means they are counting exclusively pregnancies that are untypically early. A more accurate summary of the results would be:
Bullies have more accidental children before reaching the age where the average couple will start to deliberately get pregnant.
No, a more accurate summary of the results would be: "we generated a tiny bit of data from which no conclusions can be drawn, but it's some extra data that other studies may be able to use in the future maybe".
[1] https://psycnet.apa.org/doiLanding?doi=10.1037%2Febs0000374