If you can suggest some other OpenGL games, I'm open to trying.
More info: this issue is intermittant. What the issue looks like is if I hit alt-tab, the cursor changes to my default windows cursor, which I can move around. If I alt-tab again, the cursor switches back to the game.
While I typically try to alt-tab when the game is paused, if I experience the issue and unpause the game, alt-tab brings up whatever window is next in the list. If I pause it again, alt-tab continues to work correctly.
I'd like to take back my windowed/fullscreen comment. When I move the cursor to the top of the screen, or sides, it doesn't change to the 'your cursor is over the edge of the screen'-cursor, which is why I said that "windowed mode doesn't work". However if I move it to the very bottom of the screen, the cursor changes. So I was wrong about that: my bad.
What also confused me, though, is that hitting the Windows key has no effect while the game is running, even while in windowed-mode, which is contrary to how other games operate. I play most games in windowed-mode, and usually the Start Menu will overlay the game. It doesn't do so in this case.
Just providing more info in case it might help...