Many arcade games from the mid-80s allow players to use vehicles to run over mooks — some examples include Ikari Warriors (tanks), Top Gunner (jeeps), and Speed Rumbler (modified sports car). The ur example is TNK III, a tank battle game where not only are you allowed to run over enemy soldiers, you have an incentive to do it because running them over actually refills your Life Meter.
One of the earliest examples of this trope in any video game is the arcade game Death Race from 1976, where the whole game is chasing down and running over people fleeing your car. They scream when hit, and a tombstone appears on the screen to mark the kill. Ostensibly they're supposed to be gremlins, but with the primitive graphics of the time they just look like little people. The fact that the game's working title was "Pedestrian" doesn't help.
In Phoenix, there are stages featuring large birds that hatch out of eggs, grow to full-size, and come swooping down trying to crash into you and kill you. When the birds are full-sized, you can earn points by shooting them in the body, killing them instantly, or shooting out their wings, which wounds them for a few seconds until the wings regenerate. Whereupon you can shoot out their wings again for more points, and again, and again....
Paperboy The game where everyone on the block who doesn't subscribe to your newspaper is a target for unchecked vandalism. Smash their windows, shatter their porch lights, knock over their statues, destroy their shrubs and planter boxes, or run over their flower beds... don't worry, you won't get in trouble! Complete all of your assigned deliveries successfully and they may take out a subscription themselves, even if you broke every window in their house yesterday.
There is a strong implication that the subscribers on your route are not so much interested in the newspaper as interested in not having every window in their house broken on a daily basis.
Angry Birds Space involves a lot of orbital bombardment, especially on asteroid-heavy levels.