Can we think of evolution as stable?
Certainly.
Stabilizing selection is the most common type of natural selection. There are other types, but evolution can certainly be a stabilizing force, favoring the optimal value of some trait and selecting against deviations.
And if it is a strategy, does that imply intelligence?
Not at all. Cycling lynx and hare populations follow the predictions of a differential equation better than luck would allow, yet none of them know calculus. Game theory is a way to describe patterns that naturally arise in the competitive and cooperative behaviors of organisms, not because the animals think them through, but because other combinations of behaviors don't last.
And does a mathematical game require more than one player?
Yes, by definition.
That said, a "player" in a mathematical game isn't necessarily a single person or organism. Whatever entities are competing in the game are called the "players." That could certainly include groups competing against other groups, and I would imagine various interactions between cells within an organism might be modeled as games, though I don't know of any examples.
And if it requires more than one player how is the form of the game determined?
The game is just a mathematical description of some situation in nature that fits the criteria for game theory techniques. The form of the game is dictated by the situation it's modeling.
And is there such a thing as a stable equilibrium in nature?
Go outside and look at the moon tonight.
Tomorrow night, go see if it's still there. :)
The equilibrium between gravity and centripetal force that holds the planets in orbit is just one obvious example. (A real nitpicker could insist that any system involving acceleration, including orbiting planets, must expend energy, which is lost into space, and that eventually the system would bleed out enough energy that the moon very very very slowly spirals down into the Earth and crashes after some untold billions of years. But if we define "stability"
that narrowly, there's almost no use for the word in any context.)