I agree and disagree at the same time here. Another trayicon does seem annoying but it depends if it has useful stuff on it or not, as well as being an easy way to see if lutris is running when it is minimised.
I suppose if you are sticking to the GTK and Gnome way of working you may as well go with that, I find the gnome desktop moderately attractive but not convenient to use and I can't see me going over to that system. As for the right clicking the application icon thing, that only works in that "mac os docker" style of desktop, again, not to my tastes. If you minimise on a system without that or a task manager then you can lose track of things that are running.
That said I am running KDE Plasma again as I have had some issues with games messing up the screen resolution in i3wm so it is not affecting me there (with the task manager, which I don't really like either ). I feel like there is a better solution out there using a lot of the good ideas available but no environment has it quite right.
I suppose you could look at a system tray as a version of the "docker" for certain apps as well.
I think at the end of this rambling I am as unsure as I was at the start