Power saving and screensaver trigger with some Wine games

Hello,
I'm currently playing The Witcher 3 through Wine and I've noticed something annoying: if the screen power saving and/or the screensaver are enabled, they trigger while I play, meaning that the system appears to be idle.

It's the first time I've encountered this with a Wine game. Haven't either with native games or Windows games on Steam through SteamPlay (Wine implemented in Steam Linux).

Any idea what could cause this and if it can be fixed without having to disable power management and screensaver altogether?

EDIT forgot to mention that I play with a XBox 360 controller. Other games I've played recently with Wine used the mouse + keyboard and other games where I used the controller were native Linux games. So, I wonder if Wine handles the controller in a way that the inputs are "invisible" to the DE?