GCTA does not assume that SNPs cause the trait, only that they are linked with the causal genetic material. This could even be cross-generation-heritable epigenetic annotations.
GCTA does not assume any sort of atomic gene concept, only that individuals share inherited stretches of DNA. It is true that the realities of DNA turned out to be more complex than the structure inferred by classic genetics. What “gene” means is now rather up in the air, but this doesn't in any way undermine the idea that inherited genetic information explains the great similarity between all humans and the greater similarity of closely related humans. There is an emerging consensus that changes in non-coding DNA are extremely important to the differences between humans, other primates, and plants. Is this a “gene” or not? Dunno.
Do epigenetics, mosaicism, and so on free humans from the tyranny of genetic determinism? They do mean the picture is more complicated than one might have supposed, but all along we knew that organisms adapt to their environments, in part by regulating gene expression. Insofar as these are adaptive mechanisms, they are mechanisms of gene regulation. They are keyed off of non-coding DNA, mediated by proteins coded by other DNA, functional RNAs expressed from DNA. It's true that it's a huge mess, and will resist understanding, but that doesn't mean we should give up.
Identical twins are conspicuously similar to each other in many ways, more similar than ordinary siblings or “unrelated” people. Twin studies attempt to quantify this, and in doing so make use of assumptions of varying plausibility. The conclusion from these studies of low gene x gene interaction (epistasis) is particularly puzzing, because at the micro scale biochemical processes are strongly interacting dynamic systems, and even classical genetics has non-additive dominance.
Genome technologies will continue to cast light on the mechanisms by which our heritage underlies human diversity. GCTA is certainly not the last word, but of the current technologies seems to be the most relevant comparison to classical heritability techniques. Important next steps are using full sequence data to unpick the assumptions of linkage between SNPs and unknown nearby causal DNA.