I've seen other games on Kong with some features disabled, and even some where clicking the disabled button goes to the main page; the problem here seems to be that the button itself doesn't indicate that it goes to the main page (you have to look at the bottom of the game screen to see that) -- and so some players click the button, end up logged in on both sites, and don't realize that the two windows are overwriting each other.
If the interface can't be changed to prevent the confusion (and probably even if it can), then both Kong-Elements and mainsite-Elements should be changed to prevent the overwrites. I think it should work in the same way as Kong chat -- connecting in window 1 automatically disconnects in all other windows, but you can reconnect in window 2 just by clicking a button (which will disconnect you in window 1, and load the data that window 1 saved instead of the data window 2 had before).