http://bugs.winehq.org/show_bug.cgi?id=20554
--- Comment #8 from Roderick Colenbrander thunderbird2k@gmail.com 2009-11-04 13:16:36 --- I can't see that much in the log. From a quick glance it looks similar to the issue seen in Heroes of Might and Magic III but also there the exact issue is very hard to find. If the issue is the same (and I'm still not sure what the issue is) it is likely a bug which my change uncovered.
I tried the demo available at http://www.brothersoft.com/games/populous-the-beginning-download.html and that one works for me. Can you check if the demo shows the same issue for you?