It will be several times the velocity that the rock had once it had entered the room. The mechanical leverage of pushing on the shutter near the hinge provides the first multiplier. The bellows effect of the large shutter area drawing air through the smaller opening provides another multiplier. The initial velocity of the rock will also be much higher before it hits the shutter than after.
It should be possible to compute the possible trajectories that would get the glass fragments to the rug in front of the bed. That would give an estimate on how much acceleration would have been required.
Kestrel also raised this, and other posters have already addressed the generality of the proposition. Once again this seems to be "a thing that might have some bearing in some possible universe": and that seems to be enough for you. But it is not enough for me. If this is actually important then give us some proper evidence in support of the idea that the wind blew the glass across the room. This does not strike me as plausible but that is merely an intuitive response: sometimes the reality is counter intuitive. I do not believe that is often true and I do not believe it is in this case because other posters have already raised objections which sound right to me. But if you can show facts which support your contention and which answer what has been said then we will look at them. Insinuation and ignoring points made against your proposition is still not good enough, however