The zoom effect is identical to the that of the Binoculars or the Sniper Rifle, but the Sniper Scope can be used simultaneously with any applicable gun.
The Sniper Scope actually has a higher ranged critical hit bonus than the Destroyer Emblem. However, this benefit should be weighed against the limited nature of its damage buff; even a Ranged-specialized character could get more benefit from the base Destroyer Emblem, because the extra damage also applies to minions.
If zoomed into an area affected by an area-buff item, the player will receive the buff even if they are not inside the radius. If they are inside the radius, zooming outside of the radius will cause the player to lose the buff. This applies to a Campfire, Heart Lantern, Star in a Bottle, and even 旗帜.