Targeting link pages by some idea, most obviously by topic like bingo, is good for you (assuming the links again aren’t to penalized or sites Google/Yahoo thinks are horrible), and also somewhat good for the linked to sites. This goes back to what I said about related sites. All the sites on one of your link pages are considered related or similar by Google, so any bingo site should see a small benefit from being listed literally next to other good bingo sites.
Also, if you link to ten bingo sites that Google thinks are in fact good quality bingo sites, it says to itself “hmm, good judgement of quality; perhaps this site is of quality too.” In other words, don’t get the wrong message here. Linking out to quality sites (again, what Google thinks are quality) is good for your rankings (though not for PR). The problems are in bogus links in and out, stuff virtually *only* done to boost rankings. Even though linking to a quality site might have part of its aim to boost your rankings, it still is also objectively useful to a human visitor. Those 10,000 page link partner sections are useful to no human.
One other thing: “I’ve read that we should focus on designing our websites for the visitor, not for the search engine.” This is a good idea in general, but one thing you need to definitely assume is that sometimes these exactly coincide, like titleling a page about blackjack odds “Blackjack Odds”. And then there are a couple things much more useful to search engines that you should use, like a site map. Even though a sitemap may be more for the bots than humans, there is certainly no harm to humans in having one.