I wouldn't say that AI War is an exceedingly potato-friendly game when you hit 5000+ ships active onscreen at once while using the Insane performance profile -- the framerate can drop into the low 20s on an Intel 2600K clocked at 3.8ghz with that combo, especially if the ships involved are ones that have more complex behaviors. However, you'll probably only hit that kind of situation on Normal caps at normal difficulty settings at the very end of the game. And maybe not even that, if you don't aggravate the AI to the point of building those kinds of numbers. Playing on one of the very low ship caps should get around that as it scales the units' stats so you get the same effective firepower, but with fewer ships flying around.
BTW I just downloaded the demo and the .exe is there, so it's got to be your antivirus getting trigger happy and deleting the .exe on its own. I have to deal with that kind of nonsense at work sometimes because our one-size-fits-all network security doesn't care that my department needs to do things that sometimes look scary, but there is a dumb trick that will usually get around it -- we change the .zip extension to something the scanner won't recognize, so it doesn't know what it is and can't open it and delete stuff. (My personal favorite is .stupid) Then the recipient just changes the extension back to .zip and extracts it as normal.
If you want to try that, I can rename the .zip like I described and throw it up in my private file locker online and PM you the download link. It's about 375 megabytes so I have room to host it temporarily.