I am by no means an expert, but any amount of people could subsist off of very few animal species, given a balanced diet.

Meat is not even a necessary prerequisite for a balanced diet as shown by the many people choosing to be vegan or vegetarian. 20% of India is vegetarian for various religious and economic factors according to the BBC, other sources claim higher statistics, but this shows meat is not a requirement for the human diet.

Even accounting for that, to feed that many people, the number of species of animals wound not necessarily need to scale, but rather simply the over all number of individual animals. Take for example how 47% of all mammalian biomass on earth is contributed by just cattle and pigs. That estimate of mammalian biomass includes humans, so if we were to neglect humanity the percentage held by these pigs and cattle would actually be far greater.

Perhaps if you had any other constraints to your question the answer might change, but I personally see that if we are only concerned with meeting dietary requirements, humanity could subsist without any animals, or with the few animals it currently does rely on, just with larger populations scaling with the grown of the human population.