Purchasing Shanghai for the Lynx was something I did to impress her. I don't know if it worked, but it at least showed her that Atari was cool for having such a puzzle game.
You have one task in Shanghai, remove all the tiles in the quickest amount of time possible. You remove tiles by matching similar tiles on the outer edge of the stack. If two tiles can be "slid" out without affecting other tiles, they can be removed. Easy, right?
The great thing about the Lynx version of Shanghai is actually the LACK of graphics. On versions where there is a higher resolution, the programmers feel the need to include so many fancy tiles, complicating your play. On Lynx Shanghai, the graphics are pared down to the minimum. Instead of seeing some weird flowering object with a number, you see a green blob with a number, which makes the matching process much easier.
As for music, that's the first thing I turn off. The title music is annoying (but Chinese sounding), and you'll be mad at yourself if you have the volume turned up loud when you start the game. The in-game tunes are nice, but I'd rather not be distracted by them when playing.
This is a thinking man's puzzler, unlike Klax or Tetris, so you've won't get anxious or mad while playing it. You are your own true enemy because you never know how removing pieces in one location may affect the game later down the line. So be cautious.
There are several tile configurations to make things interesting, but once you find one you like, you'll probably stick with it.
Shanghai is one of my favorite Lynx games. Give it a try; I'm sure it will become one of your favorites too.