So, we know that human-like general intelligence is possible because we display it right? We're pretty sure it has something to do with that soft stuff inside our brain-baskets, and how that soft stuff is interconnected. We've found computational primitives that we call neurons, so the premise goes, if we can understand and copy how it works we can engineer intelligence. Right? So going to genetics, while interesting and worthy, isn't really going up a level of 'abstraction' because we're trying to get a systems level overview here.
It is a process somewhat like studying a CPU by shocking prongs and occasionally slicing it real thin to see inside it.