"the true altruist helps without selfish motives"
"helping someone serves to establish a good-self-image, which will be rewarded by others"

Therefore not altruistic as defined by Nowak himself.

Nowak distinguishes between cooperation and altruism so I don't think there's any contradiction there.

He also defines altruism in terms of 'motive', which makes the term as scientifically vague as its common meaning.

"the true altruist helps without selfish motives"
"helping someone serves to establish a good-self-image, which will be rewarded by others"

Therefore not altruistic as defined by Nowak himself.

In the second quote, he's making an observation about the effects of having a good reputation. He doesn't say that a person is calculating this reward, and then helps others in order to achieve the reward.

Well of course the 'motives' need not be consciously calculated!! We are talking about genetic evolution, not introspective psychology. In evolutionary game theory plants or slime moulds can have 'motives'.