"This gene selfishness will usually give rise to selfishness in individual behavior."
This is a ridiculous, illogical leap, (or perhaps a quote out of context) - that if genes are selfish, that the organism will be individually selfish.
Quite the opposite is predicted by evolution - that in social animals, "selfish" genes will survive by producing "socially responsible" characteristics. (Though one could argue these "unselfish" characteristics have arisen for "selfish" reasons.)