General Game Playing (GGP) agents learn strategies to skillfully play a wide variety of games when given only the rules of the game. The rules are provided in a language called Game Description Language (GDL) and specify the initial game setup, what constitutes legal moves and how they update the game state when played, how the game terminates, and what the outcome is. In here we extend this line of research further, that is, we assume that the game-playing agent must learn the rules of a game by observing others play instead of them being provided. Our focus here will mainly be on modeling piece movements with less attention placed on the remaining game-rule properties. We define a subset of games, we name simplified boardgames, that despite constituting only a small subset of games expressible in GDL nonetheless encapsulate a large variety of interesting piece movement patterns found in popular boardgames. We provide a well-defined formalism and a practicable algorithm for learning game rules of simplified boardgames. We empirically evaluate the learning algorithm on different boardgames and under different assumptions of availability of observations. Furthermore, we show that our formalism offers at least an order of magnitude speedup over state-of-the-art logic-based GDL reasoners for fitting boardgames. The method is thus directly relevant for GGP systems.