I have some further test results: Red Alert, Splinter Cell and GTA III work without issues (at least without this particular issue).
Age of Empires II results in the same error, but only once you switch from the game menus to the game itself. In my set-up, the screen resolution of the game itself is different from the menus. Since I tested Age of Empires II in desktop mode, the resolution change should have resulted in a desktop window resize - as it did before the Debian dist upgrade. However, it now results in the same crash as Flight Simulator.