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Sorting is a fundamental computing concept. As for today, it is taught at the secondary school level. However, this kind of algorithm is an obstacle for some students due to its high level of abstraction. To prevent discouragement as well as to incorporate a fun and challenging algorithmic task, a novel tablet-based digital game, "Sorted," was created to serve the purpose. This research article embraces the neo-Piagetian framework of cognitive development and provides the theoretical-based explanation of how high school students establish sorting algorithms as a result of the digital gameplay. Twenty-three tenth-grade students, who have no proper knowledge of sorting algorithms, participated voluntarily in this study. They played the game with a multi-level design involving multiple unknowns. To later reflect on their operational reasoning and hence decision-making, the series of game actions were logged for individual empirical data. The sorting algorithm formation can be deduced from the logged sequential actions. They were coded and analyzed according to the neo-Piagetian framework to elicit the students' operational reasoning. The discovery of the relations between actions and schematic reasoning to solve sorting problems suggests the impact of a digital game on algorithmic thinking development, and, in general, the use of a game for self-learning of computing concepts.