Summary
Inspired by Slitherlink, but ended up more like Libraria.
Setup
Put a random number in each square of the grid.
Play
Each turn, draw a line on the edge of an unclaimed square, or pass. After placing, check any neighbouring squares to see if they are claimed; a square is claimed if it has exactly as many neighbouring lines as the number in it. The player with the most neighbouring lines claims the number. In the case of a tie, the non-moving player gets the number.
Goal
The game ends when both players pass in succession. Players add their claimed numbers, and the highest score wins. Draws are possible, but rare.
Balance
To offset the first player advantage, 1.5 komi (points given to player 2 to start with) seems to work well.
Name
SLLUG is kinda short for SlitherLink-Like Game.