It is because our game is made in Godot. Itch opens Godot games in new window regardless of what we choose in "Embed options" :-( And it is relatively recent change. My other game used to work in embed mode but now it also launches in new window.
Viewing post in Shadowtail jam comments
https://alexc1991.itch.io/pothole-dodge-returns
This is an unfinished project I did for a game a week for school.
It runs in Godot and developed to be used for the browser for mobile phones and for desktop usage.