Online Chess Puzzles & Games

Can one improve one's chess  by playing online chess puzzles and games other than those puzzles and games that use the actual chess board setup? For example I have found a game called Troyis which is similar to the famous Knight's Tour puzzle. It can be found at -- http://www.troyis.com.

My contention is maybe! Anyone else know of such puzzles and games? If so, post here!