Let’s start with the basics: If the outcome is a linear function of the genes , that is , then the effect of each gene is given by the gradient of , i.e. . (This is technically a bit sketchy since a genetic variant is discrete while gradients require continuity, but it works well enough as a conceptual approximation for our purposes.) Under this circumstance, we can think of genomic studies as finding . (This is also technically a bit sketchy because of linkage disequillibrium and such, but it works well enough as a conceptual approximation for our purposes.)
If isn’t a linear function, then there is no constant to find. However, the argument for genomic studies still mostly goes through that they can find , it’s just that this expression now denotes a weird mismash effect size that’s not very interpretable.
As you observed, if is almost-linear, for example if , then genomic studies still have good options. The best is probably to measure the genetic influence on , as then we get a pretty meaningful coefficient out of it. (If we measured the genetic influence of without the logarithm, I think under commonly viable assumptions we would get , but don’t cite me on that.)
The trouble arises when you have deeply nonlinear forms such as . If we take the gradient of this, then the chain rule gives us . That is, the two different mechanisms “suppress” each other, so if is usually high, then the term would usually be (implicitly!) excluded from the analysis.
The original discussion was about how personality traits and social outcomes could behave fundamentally differently from biological traits when it comes to genetics. So this isn’t necessarily meant to apply to disease risks.