Instead of using the Form component, use a Text Input and a Button.
Then, make that button a list, with max nº components = 1.
It will be a list of games, whose ID is equal to the code entered in the text input, and condition the list’s visibility to only show when the Text Input is not empty.
When they click that button, the following screen will only have the data for that game.
However, to associate each user to their answers, they will need to log in somehow.
You can do it by asking them for their e-mail, and setting a random password, or by asking for their e-mail, but calling it “username”, even though it will be the e-mail property.