For once, a study with a substantial sample size!
We know that genes play a role in how well children do in school, but there are gaps in our knowledge: is this the same for different topics in school? And can this be explained largely by intelligence, or do other genetic factors contribute?
Just linking genes and behaviours is still an area of furious debate, let alone figuring out the exact mechanisms by which those genes cause the behaviours in question. Hopefully studies like this one, that take us closer to identifying genetically-influenced traits, can also get us closer to figuring out the answer to that question.
Generalizing, look at animal behaviour for some insight. Take a typical breed to see what attributes it has. Labs are pretty consistent – loyal, happy, but destructive if you don’t keep them active. Bernese Mountain dogs for me have been similar to labs, but shorter life spans. Dachsunds have a lot of personality… I don’t think I’ve ever heard anyone describe corgi’s as smart 😉