In Play to Win: A World Champion's Guide to Winning Blackjack Tournaments, author Ken Einiger (winner of the 2005 World Series of Blackjack), writes, "Tournament blackjack adds a handful of new wrinkles to the world’s favorite table game. First of all, the object of each hand is still to beat the dealer; you can’t win without the right cards. But in tournament blackjack, players don’t compete against the house. They compete against each other. The object of the tournament is to wind up with the most chips at the end."
That's the crux of tournament strategy. Yes, you want to win the hand, but on occasion, especially during the last few hands of a round, players have to make all kinds of unorthodox moves as they jockey to beat the other players at the table.
The most important consideration in tournaments is betting position: The player who bets last has the advantage of seeing how every other player bets, before he wields his chips in such a way as to finish the hands with more than his opponents. Another important skill is having an accurate count of your opponents' chips. Knowing what your opponents have in front of them allows you to calculate exactly how much you need to bet to optimize your chances of advancing. Ultimately in tournament blackjack, as you say, basic strategy often falls by the wayside, and even card counting is generally irrelevant.
And in the end, these crazy do-or-die plays add up to the real fun of blackjack tournaments. As Ken Einiger also writes, "The tournament-blackjack yellow-brick road is weird and wondrous. Out-of-the-ordinary situations and oddball playing decisions and strange feelings about the outcome of hands arise continuously. Tournaments are more heady and exciting than the regular game."