Ive seen my two do this, and foster cats, and a friends dog ....
I think if the food has been eaten fast and literally comes straight back up the cat or dog who does the eating probably doesnt even notice any great difference .....
I
would worry if the cat who had done the vomiting was obviously unwell and the eater might then be at risk ..
Im told, and it makes a lot of sense, that way, way back in history our human mothers would have first chewed food for their babies before feeding them the pulp as there was no other means of pureeing it.
I guess this isnt a great deal different - though I must admit I wouldnt choose to have to watch
I dont think Mogs was being vile, just being a cat