I don't actually know if that's true, but my impression is the exact opposite - that pro poker players have basically parlayed a bit of initial luck into a lucrative career that really has little to do with differential skill and more to do with self-promotion.
Which, to my mind, is just as useful a perspective on entrepreneurship.
Players who rely on winnings for their livelihood do meet the author's description. In particular, for online poker players, the # of hands per year can total in the millions, and you can get pretty specific about the types of strategies/decisions that will alter your bottom line. I played poker online pretty seriously (and profitably) for about 2 years, logging over a million hands, and I definitely did no self-promotion.
Check http://www.pokertableratings.com/, a site that logs all hands played at the major poker websites. A major statistic is BB/100 (big blinds won per 100 hands), which is an oft used metric for profitability. The online poker community has a very good idea of the expected BB/100 at various skill levels/stakes, and the associated variance - it's very much a 'science'. The impression of self-promotion that you have is an unfortunate result of commercialized poker TV.
Certainly well-known poker players are happy to take advantage of any chance to make money with less risk. Therefore you'll rarely see them turn down opportunities to do an endorsement, be on TV, write articles, and so on. The ones who get that opportunity are not always the best. It is also clear that the chance to do this is a significant motivation to participate in tournaments.
However most pros make significant money day in and day out playing cash games. In fact most live on that. And I guarantee that you aren't going to make money on cash games with just a little bit of initial luck. I also guarantee that if you lack skill and play those cash games, you'll get wiped out.
And the pros who make a living online? I guarantee they have skill! The level of competition in high stake online games is much, much higher than in casinos.