Board games for two players

Backgammon. My young played it from about the age of 7 and their young similarly. It can be as gentle or vicious as you like!

Labyrinth is a good game that has been around a long time, but still available. Good for 2 players. Another based more on strategy than luck.

We enjoy Rummikub both as a couple or with friends
Have introduced family and friends to it over the last few years and they enjoyed it so much they all bought their own games.
An 11 year old is perfectly capable of playing it.

I came across a new (to me) board game recently called "ticket to ride" , based on train journeys. My daughter had come across it. There are different versions - this was the Europe one. Not cheap - around £30, I think, but fairly simple and more strategy than luck.