They are probably only applying the 700 genes as single factor interactions. I doubt all genes affect height. It only takes about 33 gene variants to have more genetic possibilities than there are people on earth. If they interact non-linearly, they are almost impossible to find by genetic surveys.

A fundamental problem with genetic analysis is that gene variants are categorical variables that often have non-linear effects, but predictive power goes down drastically as soon as you start looking for multi-factor effects. You have to narrow down the multi-factor search space, possibly by narrowing it down to genes that have a linear effect, but that could still be too large and you could easily miss genes that on average have no effect.

I wrote a critique of a paper using this method. I proposed studying the distribution of variant data's residual distance from a single-factor linear fit. Consider a variant that has a positive effect on height when combined with another variant, but a negative effect otherwise. The single-factor linear fit will assign it 0 effect, but residuals involving the variant will be unusually large, positive when the second variant is present and negative when it is not. My critique found several variants fitting this description (after a bonferroni correction), but i didnt have the compute power or time to rerun the 2nd order interactions with my findings.

But hey, I got a B on that paper, so maybe it's a terrible idea.

This is indeed a massive problem with GWA (genome-wide association), since the studies only see additive variation. Lot of interesting techniques around to look at non-additive variation. Had acquaintances working on drug-drug interactions and the genetics of skin colour; had to find some cool workarounds.

On the other hand, given that height is closely linked to metabolic conditions, and both the transcription/translation rate and functioning of every cellular component relies on metabolism, it doesn't take long for changes to propagate to simple traits like height.