Update on this.
Okay. So since everybody pretty much ignored my problem I simply let it drop and all.
But yesterday I got the opportunity, from a friend computer who is also running Windows XP Home (but SP3 and all latest updates in), to log in to AG when I was alone and bored. When I saw this game I thought it would be a good opportunity to see what it really is when it work right.
Turned out that the computer didn't even have flash installed. So I kindly launched the auto-updater for my friend to install it. I noticed that the auto-update picked the exact same version of flash than I am using... And the game didn't work either.
I think that there might not even be a higher flash version than 11.something for XP users anymore (the higher versions being made for 64 bits compatible OSes?). And this completely prevent me from playing that game simply because the developers decided not to make it compatible with it.
And that, my friend, plainly ____. It is bad enough when big companies decide to try to force you to upgrade your system so you purchase their new product... But if game producers do the same then it's even worse.