This is the classic board game Reversi as a Google Wave Gadget. Players takes turns placing white/black stones on the grid. Stones are only allowed to be placed to an allready existing stone on the board, if a stone is surrounded on either sides by stones of oposing color that stone will change to that color. the player with the most his/hers colors on the board when the board is full Wins.
Insert this gadget into a wave by creating a new blip/response, click the green puzzle icon, type/paste the url below and click Add.
http://www.creamdog.se/googlewave/go/go.xml
If you are interested you can download the source code here