We have different impressions of what a shroud is in this scenario.
A fan is round, a window is square, the shroud would fill in the portions outside the round area so that all the air the fan moved could not do a 180 and go back through the fan.
A shroud around the fan makes for 100% air displacement, a simple fan placed in an larger window opening will recycle a significant portion of the air it already moved making it much much less effective at exchanging inside air for outside air.
Think of an Automobile radiator fan, Most enclose the blades in a
round shroud just bigger than the fan blade diameter so that ALL the air the fan pulls, get pulled through the radiator, instead of just a tiny portion of it.