Answer:
The new game suggested by the police is for everyone to look out the window, or open their doors so that the fugitive doesn't escape.
Step-by-step explanation:
What the police do when Montag escapes and is a fugitive is to ask all the inhabitants, as if it were a kind of game, to open the front or rear doors of the houses or to look out the windows.
In this way, the only one running through the city and escaping would be Montag and so they could get him. Still, Montag managed to get to the river in time before anyone could see it.
This "game" resembles a treasure hunt or any type of hunt today.