I know it is right to say: The game is fun to play. (Because we can say play the game)
I know it is right to say: The park is a space for people to play in. (Because we can say play in the park)
I am less certain about: The park is a space for people to play. (Because we cannot say play the park)
The park is a space for people to play.
In speech, it’s likely that no awkwardness would be detected from hearing this sentence, especially if the context for using it is clear. On a test, it would depend on the course material that is being evaluated, but one typically plays in a park. This the most likely distinction one would encounter in an ELL classroom, as such, the sentence that uses to play in is probably the best choice in circumstances that describe the practical act of playing.
However, the sentence, as written, can be interpreted, with some semantical gymnastics, as an existential, philosophical statement. Such as:
The elided words serve to guide the reader’s interpretation. If written out with intent, (meant) combines with the ethereal nature of space to set this existential statement into a philosophical realm that tends to preclude a practical interpretation of what follows. Similarly, to (use for) play splits the infinitive to isolate its base form to emphasize that the infinitive to play can also represent play as a concept rather than a practical action.
From my head:
The angry man climbed the base of the statue to address the milling crowd. “The park is a space for people to play. We must not condone the presence of rag-tag drug peddlers that threaten the safety of our children with their seedy business!”
