Zillions-of-games does offer Kono, which certainly belongs to Korean Gonu category. But there are more Gonu-s other than Four-field Kono you offer. Indeed, there is more common Gonu played in a 4x4 board. And it is called Jul-Gonu(line-Gonu).
 
Stones move one square orthogonally, and make interception captures. Multiple captures are allowed. If one player has stones less than two, he cannot capture, so it is a loss. A stalemate is a loss, too. Repeating moves back and forth three times is a loss.
 
 
Remember captures are made only when an interception is caused by your opponent's move. A stone intercepted voluntarily is not captured. Since players cannot pass their turn, it is a good idea to make all stones 'stuck', so that your opponent must retreat. In this way you can usually win by stalemates.
 
 
Jul-Gonu is a type of Gonu, which is one category of Korean traditional board games, usually played on a board hand-drawn on the ground and with distinguishable stones, so it can be easily played without any equipments. The name of this game 'Jul' means 'line', for the board is drawn with lines. There are many variants due to regions. They differ in the size of the board, the number of stones, the initial position, etc.