It seems Wargame: European Escalation was broken for nearly two years (see this forum post) for Nvidia GPU users on Linux. The recent Nvidia 370.28 driver seems to have fixed it.
The game suffered from heavy graphical glitching once you get past the menu and into the game, but it looks like the newer Nvidia drivers have fixed it.
See an example of the glitching in this video:
It's really nice to see that older games that broke can once again be played on Nvidia + Linux. Sure took its time though.
Thanks for letting me know Jozef!
About the author - Liam Dawe