After listening to the recent AvPGalaxy podcast where The Last Supper was discussed, I've re-evaluated the choking scene.
Like many people here, I thought it was kind of a lame fakeout reference to the chestburster, but I've realized that, like the rest of the clip, it exists to illustrate the dynamics of the ship's crew. In this case, it gives us a situation that's literally comparable to the Nostromo's crew.
When Kane starts "choking," everyone stands up and the closest people to him, especially Dallas and Parker, immediately take hold of him to try and help him. You can see Lambert get knocked over trying to help when he starts convulsing. Even Ash, who has the most to gain from Kane's death, springs into action to put something in his mouth to bite on as everyone tries to hold him down during his seizure.
Compare with the Last Supper, where nobody is getting chestbursted, a woman is simply choking. What happens? The whole crew stands around dumbfounded before Walter bails them out. These people are not really prepared to handle being stuck on a spaceship, let alone starting a colony... or running into xenomorphs.