It runs badly with Intel grapic cards. GOG should tell it on their Aftershock page.
Minimum is old Nvidia GeForce FX 5700 and ATI Radeon 9600Pro.
It works best with at least GeForce 6600 or Radeon 9700Pro
(But ATI Catalyst drivers run very bad at now with Aftershock)

I would like if it's run "Badly"... It simply doesn't run!!! sigh! :(
I found that somebody fix a similar problem running the "Repair" option in the uninstall program... but the gog.com's one doesnt work! when i click on unins000.exe, it crash with an error code "0x800704b3" someting like "Network path syntax error" (sorry, i have Windows in Italian, so i think it's useless to post the exact error message :) )

Probably Windows 7 / starforce compatibility which is the culprit
I have the original running by applying the 1.2 patch
and then the 1.21 patch to fix Win7 compatibility
The 1.3 fan patch is optional, as I've just noticed it exists right now ;)
More info and patches here:
http://www.ufo-aftershock.com/pages/support.html#patches
edit: none of this need apply to the gog version, considering, drm free. So starforce shouldn't cause problems on win7 in the gog version. In that case atleast upgrade your graphics driver.

For those with intel graphics card and that cannot run Ufo Aftershock: apparentely there is a workaround using linux and wine that allows to run Aftershock in Intel graphic cards.

See this post:

http://forum.fish-fillets.com/lofiversion/index.php/t9818.html

So the limitation is windows specific and not from hardware...

Make sure your video drivers are up to date. That may fix your problem.