The claim that games provide a space for play seems to be an inversion.
Through free play games can be constructed and then ‘played’ but the resultant play is rather : use or participation.
A game is a construct, a matrix of rules and limits within which a ‘player’ can operate. Fun can be had but it is not free play.
A creative approach to a situation can involve play and experimentation; systems such as games can be generated to breed material or reflection.