Given your parameters, yes.
Chess has a specific Good, within which are themes, i.e. logical/effective matrices (strategies), within which are "successful" moves (tactics).
Life may well have various goods or goals, each potentially a type of feed-forward for an individual player's other games, with the gamer in effect not competing directly with any specific opponent. Insofar as specific goal-achieving processes are mutually reinforcing/inhibiting/or even neutral, hyper-dimensional gaming for a given individual's world-line is more probable; e.g., high school student Johnny is interested in a goal of a particular college major; he may have several, and separate, single-player games that also link together to form a uni-player hyper-dimensional game: his nutrition game, his funding game, his gpa game, etc. To analogize to chess, Johnny might have a bishop game (for each bishop), etc., within an overall and therewith hyperdimensional chess game called "be a College Major." Poor nutrition for one bishop might limit her movement range, for example. An extremely well-funded rook might have additional power (e.g., school lunches) able to help the bishop, and, linked together, the bishop and rook would comprise a two-dimensional hyper-game. Life, unlike one-dimensional (with set rules) characters of pieces in a gaming matrix, is more complex, per each game's or character role's (gpa seeker, eater, etc.) spectrum of developmental outcomes, often multi-dimensionally influencing one another. (This complexity and fluidity is also reflected in the symphonic art of the European musical tradition, which developed single-player melodic themes within a larger harmonic structure.)