It is a strange construction to get your head round, but I believe that is the correct way to express this.
It also accepts "The playing field is theirs," which bears a more immediate resemblance to the Swahili.
Still not fixed. Still no such thing as playing ground. This will continue to be ignored. 02062020
Their field... is not valid?!
But it doesn't say "their field...". It says "The playing field is theirs." (Subtle difference.)
It is called a PLAY FIELD