Yes, Nintendo actually released a mini-game called Dong vs. Dong back in 2003. Of course, the title wasn't a stand-alone release, but simply one of the few unlockable mini-games found in the title WarioWare, Inc.: Mega Microgame$! for the Game Boy Advance system. The game is multiplayer-only but it's possible to play alone at the expense of actually having fun. In 2014, the game was ported to the Wii U via the Nintendo eShop.
In the GBA and Wii U version of the title, two people hold one controller and simply press the right or left back trigger at the correct moment. Your Dong, which is just a strange wide block, penetrates blocks in the middle of the screen. You must penetrate each block with your Dong numerous times before all of the blocks are on the other player's side. Once the block hits the player's side, it can't be returned. The player will attempt to penetrate the blocks with their Dong before it can reach their side. This is a game that requires skill, patience, and timing. As mentioned, the game is 1 of 4 unlockable mini-games.
Playing the title still provides enormous amounts of fun and joy to this very day. Nintendo created a classic when it came to the games in the WarioWare, Inc. series of games. In June of 2013, Nintendo released Game & Wario for the Wii U. The title was partly inspired by the WarioWare, Inc. series, but failed to meet expectations in terms of sales and critical response. While we wait for a new game in the classic series, let's bump our Dongs together as soon as possible.