Playing creative games is equivalent to doing mathematics.
The abstract ideas developed in Mathematics are not developed for a specific use. They are just developed as natural extension of known body of logic. This new extension fits with the known set of rules of mathematics. It possibly makes the existing framework more whole by showing an underlying generality. It's thought of in order to make the existing frameworks more general, or solve discrepancies in it. It's not thought of to solve any practical problem.
In that sense, the Mathematical skills that a person might have are akin to solving puzzles in a game with creative game mechanism.
In Braid, the player is presented with the new universe where time changes in many unrealistic ways. The player is coerced to observe these new ways and discover solutions to the problem at hand (saving the character from dying).
Player does not necessarily understand the patterns, for instance they don't necessarily know the formula that governs the reversal of time in Braid, they just develop a perception that's good enough to predict how the time will behave. He/she just gets used to these patterns enough to solve the problem at hand. However different problems presented with the same mechanism trains the player's brain to get used to it more easily, learning subtlties along the way.
"in mathematics you don't understand things. You just get used to them." - Von Neumann [link]
“I am interested in mathematics only as a creative art” - G.H.Hardy [link]