If you read on in the page you link to, under the medical definitions, you would have found:
[2. b.] a waste product (as urine, feces, or vomit) eliminated from an animal body : excrement—not used technically.
Now, the definition above gives a good definition of the technical use:
[2. a.] something eliminated by the process of excretion that is composed chiefly of urine or sweat in mammals including humans and of comparable materials in other animals, characteristically includes products of protein degradation (as urea or uric acid), usually differs from ordinary bodily secretions by lacking any further utility to the organism that produces it, and is distinguished from waste materials (as feces) that have merely passed into or through the alimentary canal without being incorporated into the body proper
So, in a technical sense, vomit is not an excretion. In a more general sense used more informally in medicine (by which I suspect it may relate to the fact that cleaning it up is part of the more informal side of medicine) vomit is an excretion.
In general though, excretion (and more often excrement) is commonly used of faeces, often as a euphemism, while those who studied biology at a secondary-education level might well know the technical sense too. Neither understanding matches vomit. So while you can point to a dictionary and argue you're within the letter of a definition, it's not a good choice of word. (By all means send readers to a dictionary when the word you settle on is clearly the best choice, but that's not the case here).
Perhaps "bodily functions" would be a better choice for tag; it covers the same territory, and is less likely to meet objections around definitions.