There is not enough context to know what is going on and why they are there.
Can you give some more background?
Is this in the country, or just the angle of the shots looks like it is in the country?
Is this in season?
What happened to the deer that they shot?
Why did they pick the one that they shot?
Why shoot it with a handgun?
Were they called to the scene or just happened upon it?
If they happened upon it, did they call it in?
OR to put it another way, you have not convinced me with this video clip that anything illegal is going on. I would like to see the police use a carbine if possible so they could have made a more precise shot, but then again, I don't know the situation.
I have seen deer get locked together before. It is not very pretty when one breaks the others neck. DNR shot the one that was still alive because it was more humane than letting him starve and they didn't have the ability to shoot the antlers and breakup the lockup.