teddy should know - he is a mathematician 
Lord-of-War 
I'm a physicist, at least in thoery.
But I'll answer anyway.
This is what I read:
The M203 could engage a window sized target out to 150 meters and an area type target out to 450 meters.
The standard 40x46mm high explosive grenade has an effective casualty radius of 5 meters. The effective casualty radius is defined as the radius of a circle about the point of detonation in which it may be expected that 50 percent of exposed troops will become casualties. Safe-weapon practices for firing the M203 grenade launcher require a minimum safe distance of 130 meters for high explosive rounds, and 165 meters for HEDP. Range regulations stipulate that all targets have to be more than 200 meters away. The danger radius of the high explosive grenades is 130 meters (427 feet).
I have seen people firing up straight in the air behind arch or stairs and the dropshot only comes down after a significant amount of time - so this to me doesn't make sense if the first sentence (blue) is true. The dropshots that are fired straight up in the game must actually travel
a few kilometers taking the time it takes for them to come down.
I don't think the launcher has the strength to perform such shots.
And these shots I would define as the dropshots in question cause they are being fired at an angle of 75 degrees or higher
So in my opinion these dropshots (in real life) are a bit far fetched - correct me if I am wrong
Lord-of-War 
I don't know exactly where you read this, but I hope it's a reliable source (it does look reasonable and wikipedia reports similar numbers).
What you need to understand is that the range you were reading about is effective range. That is the range at which you could actually engage a target.
It doesn't mean the M203 will not travel further. It means you would not expect to hit anything. At least in real life.
Now, shooting it straight up or even at 45 degrees is something that probably something nobody in a combat situation would do. Straight up is just firing at yourself and at 45 degrees you really wouldn't know where it lands. It will probably go significantly further than 450 meters, but since it's not practiced for more than 450m, you will probably have no clew where it lands.
As for shooting straight up, I know it takes quite a long time to come back in the game. But it is expected. The 203 looses it's momentum going up until it gets to 0 and then it starts to gain momentum towards the ground because of gravity. All of this will take quite a while.
I also know that the US Army used actual weapons to make this game, so I would expect the intial velocity of the projectile is what it is in real life (or close to it). I doubt air resistance is taken into consideration in AA, but it doesn't really matter that much.
Both the initial velocity as well as the maximum height can be directly calculated from the time it took for the 203 to fall down (without taking into account air resistance and assuming the same gravitational constant as in real life).
EDIT:Fixed a few idiotic things
