I tried to use 'thinking analytically' to describe the calculation-evaluation cycle that is present in so many strategy games, especially chess-style games. I guess it wasn't a very good descriptor. Anyway, it's too late to edit it.
The typical chess mental game involves chains of calculations to visualize future positions, then evaluating those positions based on the potential of good or bad chains of moves. "Strategic" plays are based on the possibility of generating or preventing future tactical plays.
Bridge is more a game of inferences; out of the 26 or 39 cards you can't see (depending on the phase of play), the most important part of the game is guessing how those cards are distributed and planning for the contingencies that might arise (or the ones you need to arise). There are very few situations that involve long chains of calculations and possible positions; most of it is planning correctly, estimating probabilities (unless you're one of those talented people who can do the exact math in their heads), and good guesswork. Or at least that's how I play it...
It's very refreshing to play a game that works out those areas of the mind, which are so important, but for which there are few direct workouts. The best play is usually clear post-mortem, and hands change every 7 or 8 minutes, so you get a lot of quick, direct feedback.
The second most important part of bridge is communicating with your partner based on the limited language of putting cards down on a table, and the reason it's not the first most important part is because communicating correctly depends on inferring correctly, planning, and understanding partner's plans.