...Just the same. Just note that this is open play and not the cutscene. Write all events, but note which part is a cutscene, which is a dialogue, which is plain action, which is a quicktime event...
In case of linear games this is very simple, and doesn't differ from typical script by much.
Now, in case of games with more advanced plot, the scripts are branching. There are elements that are optional, may or may not have impact later, depend on prior decision or cause total script split into two or more entirely different realities.
First, tag your scenes/variants, and whenever the plot branches for longer than a couple paragraphs, present
"if [condition is met], proceed to scene#. Otherwise, proceed [to next scene]".
Then, all (except 'decorative', illusory choice) decisions the player makes in game that impact the plot in the long run, can be represented by 'tokens'. Tokens for items possessed, tokens for knowledge gained, tokens for switches toggled etc. So, if the player makes a decision with lasting impact, generate a token to be used when the 'impact point' is met. Whenever you arrive at such a branching point that depends on a prior decision, include respective token in the condition.
"Player may choose to check under the stump, finding BAG OF GOLD
Player arrives at the gates of the mystic tower. A hatch in the gate opens, eyes of an old wizard can be seen.
PC: I need to learn magic.
WIZARD: Pray tell me, how do you intend to pay for such lessons?
If the player has BAG OF GOLD, proceed to scene #72, otherwise:
(script about turning the player away follows)
A concept map graph is immensely helpful in arranging the scenes and their dependencies.
Note if your game is of 'open world/sandbox' type, you can manage the script easier by splitting it into multiple plotlines - "quests", which should be quite independent from each other (or creating few, clear dependencies). In this case sequence of scenes is assured only within the plotline, but different plotlines may progress at different pace independently and simultaneously.