What are the implications/predictions of the selfish gene theory?
The Selfish Gene theory "can be defined as the idea that the gene is the ultimate beneficiary of selection".   Argren, in Selfish genetic elements and the gene’s-eye view of evolution lays out the history of the theory and the arguments for and against it.

The theory is almost certainly correct; and it's almost certainly incomplete. The theory is testable.  It predicts, for example, that there will be genes whose sole function is to self-propagate.  Those genes can't confer much fitness disadvantage to their host or they will quickly be weeded out of the population; and they don't necessarily need to confer a fitness advantage. But to the extent that different individuals have different versions of the same genes, the versions that convey a fitness advantage are likely to win the evolutionary competition.

There are, of course parasitic genes like transposons which impose a cost by requiring the host to adapt to their presence.  As long as the host is able to adapt without losing too much fitness, the parasitic genes can ride along for free. 

The Selfish Gene theory provides useful insights, but it is incomplete, because combinations of genes,  arrangements of genes, and even genetic diversity within a population can provide a fitness advantage or disadvantage. Even genes are subject to "group selection", where gene A can provide a disadvantage unless gene B is also present, in which case A and B together provide an advantage. This leads to selective pressure to link the two, e.g., by placing them close together on one chromosome, which is analogous to a cooperative relationship between the genes that provides a mutual fitness advantage.