Let me use an example.
Most are familiar with tic-tac-toe (TTT). Normally, TTT can be recognized by its well-known crosshatch playing field and its conventional playing pieces: Xs and Os. Yet neither of these two game elements — field or pieces — is critical to the formalist. The most fundamental property of any game, according to the formalist, is the relationship among game elements. In part, this relationship is described by the rules of the game; but the rules of the game may be expressed in different languages and in different ways. So, again, the surface appearance of the rules — whether these rules are written in, for instance, French or English — is immaterial. It is what the rules refer to, not the rules themselves, that constitutes game form.
Imagine another game (let’s call it T3) consisting of nine tiles, labeled a1, a2, a3, b1, b2, b3, c1, c2, and c3. In the game of T3, two players alternate picking tiles, attempting to select tiles that will create either an a-b-c sequence, a 1-2-3 sequence, or both. The game of T3, without a crosshatch playing field, without any Xs or Os, is formally identical to TTT. For the formalist, the elements of TTT and T3 that are dissimilar are inconsequential, and the parts of TTT and T3 that overlap are fundamental to an understanding of the game.
One technique of the formalist, then, is to identify and distinguish fundamental game forms, commonly found in rules-based relationships among game elements. However, while these forms are referenced by game rules, they are not, in all cases, determined by game rules. That is, formal relationships among game elements can be extended to include relationships among games and their players. Game form can then only be fully realized and known during interactive game play.
Since formalism is concerned with the relationships among game elements rather than with the game elements themselves, formalism is rightly concerned with abstractions. These abstractions are, simultaneously, references. And, therefore, formalism is ultimately concerned with semiotics, or the science of signs, symbols, references, and all those rules, explicit and implicit, governing their use.