I've had never played with Catan even though it iswas so well known (popular) toamong young people enough that a Catan club was established in mywhen I was in college days.

In this sentence you say that you've never played Catan, but in the next sentence, you talk about how you played Catan in the past.

I've never played Catan ... A while ago, I played Catan.

"I've never played Catan" has the implication that you've never played it before / in the past / in your life. I think "I had never played Catan" is correct because it has the implication that at one point in your life / in the past, you had not played Catan.

A while ago, I played with Catan which my friend brought during a camping.my friend brought Catan along on a camping trip and we played it together.

It was a more exciting game than I expected!

Though I haveit is difficulty to playing board games without getting together with my friends, I'm happy to know how to play it.

I've never played with Catan, even though it is well known (popular) to young people enough that(there was a Catan club was established in mywhen I was in college days).

A while ago, I played with Catan which my friend brought Catan during a camping. trip and we played.

You can also do "I played Catan, which my friend brought during a camping trip" but it sounds akward.

It was a more exciting game than I expected!

Though I haveit is difficulty to playing board games without getting together with my friends, I'm happy to know how to play it.

I've never played with Catan even though it is well known enough (popular) to young people enough that a Catan club was established in my college days.

You play games, you play with objects.
For example:
I play chess.
You play checkers.
I play with the ball.
He plays with the chess board.

A while ago, I played with a Catan board which my friend brought during a camping trip.

It was a more exciting game than I expected!