The meaning of the name:
"Puzzleshipping" is the pairing name for Yami No Yuugi and Yuugi. Shipping, as you obviously know, in anime, refers to a pairing, love triangle, or just about any other kind of anime pairings. Puzzleshipping is the name given to Yami No Yuugi x Yuugi because they first met within the Sennen Puzzle and they bonded because of that Sennen item.
About this Fanclub:
This pairing is the cutest Yuugiou pairing in my opinion. Thus, this fanclub. ;P