This actually ties in to some more general issues, so I'll start with a brief discussion of them.
The first parallel I thought of is suicide, which like genocide is mainly used as a noun. The corresponding verbal expression is normally to commit suicide; it's relevant that the verb to suicide actually is attested, although it's extremely rarely used and clearly not the preferred option. (See the following questions: Can one conjugate and use 'suicide' as a verb?, Difference between “commit suicide” and “suicide”)
Possibly more relevantly, the OED also has a couple of citations for homicide used as verb, one from 1470 and one from 1858.
The word genocide was coined relatively recently (in the 20th century), and the OED only has an entry for it as a noun.
Here is a Google Ngram chart comparing relative frequencies of suicided, genocided, and homicided:
My conclusion is that
- For all of the nouns with the structure X-cide, the normal way of constructing the corresponding verbal expression is commit X-cide.
- Sometimes, but quite rarely, we see people simply use the noun as a verb; this is attested in the OED for suicide and homicide, but not for genocide. This seems to be most common with suicide; possibly, as mentioned by some people in the linked questions above, this is due to a desire to avoid using the structure commit [some action] which carries a connotation of criminality.
I agree with the others who have said that genocide used as a transitive verb is understandable, but sounds ineloquent and informal or uneducated.
When you use the expression "commit genocide," you can't have a direct object. The equivalent to "I genocided over 16 types of monsters" can be expressed in more than one way, but you need to use a preposition of some sort.
The first I thought of, and the one that has been most commonly used according to the Ngram Viewer, is against: "I committed genocide against over 16 types of monsters." Other options include commit genocide on and commit genocide upon.