Just a couple of notes, this has nothing todo with laptops per se, only small screen size or rather a small resolution.
Second I sometimes play with my work laptop with 1280x800 (compared to my home 1920 × 1080) and have never had any such problems, the flash seem to resize according to the available working space you have and I never been forced to play full screen.
With that being said, can someone post the minimal requirement for resolution for FOE?
Also there is a similar long standing issue, that you can't see the towns top most corner (has nothing todo with resolution, but FOE map)