Only language?
Now, it is a preexisting society with already established rules, customs and history. People who have generally followed a way of life, would indeed follow it... At least for a short while.
As mentioned above, physical gestures, body languages, and trust from knowing how each other acted would go a long way in a situation without language.
So the key here would be if they can last until they kick the @ss of the BBEG who caused this, or create a new simple but functional language that at least convey the bare minimal meanings...
If EVERYBODY behaves.
(And we don't want that cause that's borrrrrrring. v=w=v )
==========
Now, the most basic idea: What would the lost of language brought to a society?
1) Confusion.
2) Disruption of everyday activities & decisions.
3) Openings.
If most of the guards are of one race, people from other races would suddenly become easy victims because they would have no way to report crimes, and guards from those races might be too few to coordinate effectively and you could just outright take them out through sheer numbers; Criminals would just have a field day if you couldn't properly describe them.
If a race was not viewed positively, this would be the perfect moment to push your negative ideologies upon them since they could no longer defend themselves.
If your race did not have a central figure, this would be the best time to take that with whatever means un/necessary.
Disruption of services meant that not everyone could get the help they needed. You could use this to help your own to bring them under you. Or you could help another race to milk points because everybody still have eyes, and you just needed to make it very visible.
Got a grudge? Didn't matter whether its your race or not. This was a confusing time, its easy to create openings for schemes or even something lethal.
Politics its even worse. There might be a central power in your region, but now that would be splintered by as many races in as many areas. Time to take lands and hold them.
========
It might seem like a small "cut the BBEG and done" scenerio. And it could be.
But it could also be a massive city/political/revolutionary campaigns that's Game-Of-Thrones dark.
Just how you used it. v=3=v
(well, just imagine what would happen if we just lost the internet right now.... No wait, that'd be much, MUCH, worse. Nevermind. !!!=_=\ )