It seems very thoroughly accepted - among researchers who have studied the subject. The popular press produces a lot of articles downplaying the subject. For example, if a study shows that IQ is likely the result of thousands of genes combined rather than just one or two, there will be ten articles the next day saying "scientists unable to find genetic basis for IQ" and "IQ not genetic."
I am not questioning that IQ might well be a genetic factor, just wondering if there are any conclusive studies that it's directly inherited. Because the study you linked is very open-ended on this, and this has been core premise for the article discussed.
This is not genetic but not "necessarily hereditary", this is hereditary, but requiring a combination of inherited "things" to manifest. (The typical simple case of "Mendelian trait diseases" to which this applies are recessive traits, which require inheriting a copy of the gene from each parent to manifest.)
IQ, not being a binary trait, doesn't work the same way, and probably (even to the extent it is genetic) the product of isn't a single, simple genetic trait of any kind, but influenced by a number of different genes. And, also, influenced by lots of environmental factors (and it may turn out that the way in which some of those environmental factors contribute depends on which combination of genetic factors are present.)
There seem to be big differences in correlation between identical twins and fraternal twins, which is a pretty strong indicator there's a genetic component.
1) IQ "capacity" is genetic, and, as such, inherited. (Though its probably not a simple single trait, but a consequence of interactions of multiple traits.)
2) That actual IQ depends on both genetic capacity and a large number of environmental factors.
