As much as violence is discouraged in today's culture, both Super Mario World and Kirby's Adventure display their form of violence to increase your chances of success in the games. Although some or all levels do not require you to be violent, it can be in your best interest to commit violent acts to improve your chances of winning.
Take Super Mario World as an example. Playing the very first level provides an immediate "fight or flight" situation for the player. There is an elevated slope platform in front of the player with a Koopa on top of it. The Koopa immediately slides down the slant, quickly approaching the player. It then proceeds to chase you unless you choose to do something to handle the situation. This can be done by simply avoiding the Koopa, but he could eventually return. What most players opt to do is to jump on top of the Koopa's head, ending his time in the game. Not only does this create a more comfortable situation for the player, but he/she is also awarded points for defeating the enemy. Also, if you can terminate some Koopas, they will leave behind their shell, which you can then pick up and throw at other enemies in the game. Therefore, the game is trying to influence the player's decision-making by giving the player points for committing a violent act to improve their chances of success.
Kirby's Adventure also shares some of the same characteristics as Super Mario World. While less violent, the game still provides a way for the player to remove enemies from the game using Kirby's ability to consume. Kirby's ability not only removes enemies from play, but it can also provide him with powerful abilities depending on the type of enemy Kirby consumes. This provides an edge for the player to help them win the game, but it also gives the player an idea that committing such actions provides them with only good results. Kirby's Adventure, along with Super Mario Bros., gives their players the wrong thoughts about violence and how it should be handled in society by rewarding players for being violent in-game.
I found it thought-provoking how you described the Koopa as stimulating a "fight or flight" response for the player. It suggests that one's feelings for survival in the game can translate to similar stresses in real life and shows how strongly players can be connected to a character, even 10 seconds into the game without knowing anything about the character. It's this aspect of video games that I find to be the most compelling, the psychological aspect of them. By not only being rewarded for the violence but also depending on it for survival, players can quickly become invested in the game, character, and acts of violence in order to progress.
However, I do agree with the other commenters…
I agree with erikkerrigan's comment regarding the difference in violence portrayed in these games relative to what we may see today. In both of these retro games mentioned, the method of 'killing' the enemies encountered is regarded as something that can only be done in game. Unlike GTA for example, where the violence, fighting, and combat mirrors real life, I find Kirby's 'attack' move of inhaling enemies and turning them into a star when spitting them back out to be so un-realistic it is not associated with violence. Likewise hopping on enemies or throwing fireballs in Mario is different enough that the violence I feel does not translate to how we think about our actions in our life.
While I do agree that the actions can be inherently violent as a way to "kill" an enemy, I believe that the games do a good job of removing as much of the violence from the actions as possible. For example, while consuming enemies, the enemies will just disappear. There is no visual of them having a "death," and they are simply removed from the screen. I think this lack of emphasis on the deaths can desensitize both the player and the action in an objective sense, rather than an interpretive one.