If you play one account in two different windows, you will lose progress at some point. So go ahead, waste your time.
Great...you are so nice to new players who don't even know about this.
At least put a warning message on the login screen or something. Unless the game says you aren't supposed to do it, SOME PEOPLE WILL DO IT. Either by accident (leaving the window open then starting up the browser later again and playing there), or intentionally (Shared accounts). And unless the game says they aren't supposed to, it IS CONSIDERED A BUG, WHICH IS THE DEVELOPER'S FAULT, because players do nothing they aren't supposed to do.
Adding "Playing the game in multiple computers simultaneously from one account can result in lost progress" to the login screen is the absolute minimum you can do for your players, if you are too lazy or for some reason unable to check for double logins.
By the way, is there any way to split an account into two? Is there a way to change the password? No, so I'm stuck with sharing it. I'll solve the problem by limiting the time of the day when each of us can play, but you shouldn't intentionally let others waste their time when all it takes is a warning message.
(From the perspective of players...I lost a day of progress to a bug? He, they knew about about it and didn't fix it? Time to look for another, more stable game... I bet you don't want to lose players on this so put up that warning message!)