Lariat (PDF) is a familiar-feeling abstract game rule set from Mark Steere Games. You simply have to either join the center to the edge with a connected row of stones, or join the center to a ring that surrounds the center. Mark claims, and it seems to be obviously so, that one player must win, just like in Hex.

The twist is that the game is played on a hexagonal cylinder. How exactly, I’m not sure. I assume either using an online representation, or with magnets.