In my case, it appears to be a problem with handling of dual monitors. I found the Configuration.txt file at my Home directory in My Games/Lords of Xulima/, but it showed a graphic width of 3600 pixels. I changed it to 1920 pixels to match my main monitor, and now the main screen loads normally. I can play the game.
Problematic, though, is that I simultaneously lose all display on my second monitor because it gets deactivated.
And after I exit the game, I have to go to system preferences to activate my monitor again. So I'll consider this change merely a workaround to play the game instead of a proper fix.