Everything can be seen in the picture.

Is this i3? It probably ignores that Lutris can't be squished to this window size.
It's more of a problem with i3wm than with Lutris. Lutris usually can't be resized like that, but i3wm doesn't care.
I'd recommend configuring i3 to always open Lutris as a floating window. To do that you have to add for_window [class="Lutris"] floating enable to your i3 config. In case you also encounter issues with Wine, I'd recommend you to enable Winedesktop globally and set Wine applications to always open as a floating window (for_window [class="Wine"] floating enable)
This cant really be fixed on the Lutris side, since i3 does not respect the minimum window size in docked mode. You can make the windows as small as you want. It is only respected in floating mode, as Medath already mentioned.
Closing for above mentioned reasons.
Most helpful comment
Closing for above mentioned reasons.