Seems like a pretty wild assumption to make. Maybe they need that to simplify their model, but still...
This study follows in the path of past twin studies looking at even narrower outcomes (notably IQ, which is a little reductive but has relatively well defined measurement, and where inheritance is almost entirely genetic). But this is still only tickling the surface.
Anecdotal: having both biological siblings and an adopted sibling in our family from a few months of age (and knowing the biological father of the adopted sibling), it seems very obvious to me that the main mechanism of personality trait inheritance is genetic. (Assuming no calamitous abuse, trauma, malnutrition, childhood illness, obesity, substance abuse... or similarly devastating lifestyle patterns that can propagate across generations and do impact personality.)
Some more context for setting sensible priors/ expectations: humans are just animals. We recognise personality traits and behaviour patterns in particular dog breeds (and of course all domesticated animals) - we actively breed for such traits. We know that these traits persist and continue to be inherited irrespective of animal parenting. It would be absurd to expect that genetics aren't a large part of the explanation for variation in personality traits and behaviour patterns within human populations; and also for their heritability and for variation across distinct human populations with historic barriers to gene flow.
What's missing, of course, is more rigorous and more granular definition of traits - and then measurement, and data collection.
We're also missing a more direct attribution to the underlying genetics (sequenced genomes, activations...) - though data there ought to become accessible.
Of course, low level personality traits influence behaviour, habits and decisions in a manner mediated by our environment, nutrition, activity, stressors, hormonal fluctuations, social institutions, narratives, learned perception and learned actions/ skills (where patterns of thought are a type of skill too!).
There's my outline inference, reasoning & expectations. It would be nice to see a framework of more rigorous definitions, data collection channels and falsifiable hypotheses - to more robustly expand our understanding of human nature(s).
With all knowledge, there is the question of how it might change the world. The ability to make better personality or (limited) behavioural predictions about a person based on genetics, could be profitably (ab)used in setting insurance premiums/ deciding insurance eligibility, in dating/ partner selection, in recruitment, in provision of better (psychological) healthcare, in providing better (and better individualized) education, in providing better (customized) advice for people to improve their lifestyles, habits and outcomes, in selective IVF, in the migration policy of nation states or in some sort of active eugenics program. Many of those would seem ethically problematic! That's perhaps for democracy & legislation to address - later, once patterns and mechanisms are better explored and modeled.
Separately from the practical applications, a better understanding is in itself good - we should want to understand ourselves; we should seek the truth. It's a shame this sort of research is (still) so controversial. Tooling progress (especially sequencing and neural networks, where neural networks have a role in trait discovery/ measurement and in inference) will most probably drive this field forwards in coming decades, irrespective of controversy.
As they grow older their instinctual inclinations are tempered by cultural and social norms and by whatever reinforcement style the parents and teachers employed. Even entertainment like cartoons and the internet constantly impart cultural lessons upon them.
They are constantly being told what is right and what is wrong, what is good and what is bad. Even though they might not necessarily feel like they agree with it. And that is what shapes their morals, which in turn shape their behavior, which in turn shapes their growth, which ultimately shapes their intelligence.
If they developed some behavioral or mental issues, they will learn coping and masking mechanisms to compensate. If they were rewarded for something they were naturally proficient at, they will learn to excel at it.
So I don't see how it's so easy to settle what is obviously not even a debate. Both nature and nurture are important in varying amounts at different points in time because the world is complex.
As for intelligence, it's not surprising to me that some people are just born smarter than others and that this trait carries over genetically. It's how intelligence evolved in the first place. But with persistence and a positive environment it's possible to overcome many unfair setbacks in life (and vice-versa).
Our offsprings are completely helpless for the first year. We aren't as fast, strong, or resilient as most wild animals; So we had to compensate with something. Our total weakness pushed us to use our brain to survive. For example, open confrontation without a plan, even with a pray animal like deer, would result in a total failure. Yes, we are in part endurance hunters, but no amount of endurance would help with something that's categorically faster than you. So we hunted in groups, using tools and schemes to survive.
And here we are now.
Conversations about intelligence, imo, often miss an important caveat. Humans have a unique ability of plasticity, this constant adaptation and growth that all of us are capable of in a single lifetime. I'm of opinion that if you are capable of speaking a language, that means you are capable of learning and understanding anything. Information, ultimately, is causal relationships and compositions; The more you can see and meaningfully categorise given the circumstance, the more 'intelligent' you are; More specifically - how much can you transcend your cognitive barriers - the way things can be thought of, [permissible/assumed to be valid] modes of engagement with what you experience so to speak.
We sometimes corner ourselves into limitations to maintain a sense of comfort, validity, and alignment with what we think "actually is"; Rather than accepting and understanding things as they are without any stakes and generalisations.
Point I'm trying to make is, sometimes intelligence is stagnant due to inner dissonance, conflict, alterior to understanding motives. Apart from complex motivations varying from person to person, things like malnutrition, and trauma that takes up cognitive bandwidth and sets limits on cognition, also affect us; What we even think of as good and bad, everything we are that we accumulate over the time of being alive - affect the way we think about what we are experiencing. Let's not forget the effects on who you are during developmental period in womb and the circumstance of said womb (overall hormonal and chemical circumstance).
I believe, in some cases, we are eager to explain intelligence away as mostly genetic because it's easier to understand variance that way, rather than having to swift through circumstantial nuances and complexity; Sometimes as means of not changing anything about ourselves and our conduct with eachother, the way we organise; Sometimes to maintain a sense of superiority and inferiority relative to others. List goes on.