The fullscreen is fullscreen in the sense its window is fullscreen. And no, it does not always mean it is also stretched to the dimensions of another device.
When gngeo is in windowed mode, its resolution is still the same, meaning the lower part of the screen is not visible. This means you can't see the save/load dialogs.

Usuallly fullscreen has better performance, but I think in the case of gngeo there is hardly any difference.

I removed aes-bios.bin to check and I could still start gngeo, that's why I know.

It still could be I attached a wrong version in the deb file. Will check that later.

edit: Nah, version is correct, as I expected. What version of gngeo does the application manager tell you have installed, the 0.7.0-3 version, or an older version?