I doubt you'll be able to solve any puzzle with a meme, so no they aren't that important. (But they are awesome!)
As far as Japanese only items, there are plenty of things they have that we don't. I'm most familiar with traditional Japanese toys, so I'll use those as an example:
Hagoita - Paddle Used in a game called Hanetsuki, which is sort of like badminton, but the paddles are wood and there is no net. The paddles are also beautifully painted or have silk collages on the backside.
Daruma Otoshi - A tower of wood discs that are knocked out by the player from the bottom up, and you must not topple the tower.
Menco (or Menko) - Similar to pogs but they are flexible cards and you throw them next to others to try to get the gust of air to flip the other card. (Better explained in slo-mo video form:
http://www.youtube.com/watch?v=5CJ70Mm6P14)
Take-Tombo - A wooden, or bamboo, propeller stick toy. Literally translates to "Bamboo Dragonfly", you hold the stick part in your hands and move your palms in opposite directions to spin the toy causing it to fly into the air. (Picture example:
http://www.goodsfromjapan.com/images/product/248/image4.jpg)
There are lots more obviously.
I suppose with most of these you could get away with "paddle" or "card" or something generic, but theres plenty of stuff that's specific and exclusive enough that it makes me wonder how they'll handle it.
