What do you mean by “my game?”
The first thought is that he’s in “pass through mode”. If you lightly double tap on the side of the quest (I tap on the part that is attached to the strap), it will go in or out of pass through mode so you can see what’s around you (convenient for grabbing a drink, repositioning, etc). This is often also triggered when plugging in headphones/putting the set on/off.
That being said, being outside your guardian area (playing area that you yourself set) will also cue passthrough mode.
I don’t know what you mean by “my game” though. You’re playing on a separate quest and he puts a quest on? That wouldn’t let him see your gameplay. Maybe there’s a workaround, but this is the same idea as “I turned on my PlayStation and can’t see my friends gameplay on PlayStation”.
edit: I went back and fixed it, but I meant DOUBLE TAP on the side, not just “tap”. My bad if you were trying that.