"I am not an egg."
Translation:Ego non sum ovum.
In Latin, the negative particle "non" has to be directly before the noun it negates (There are exceptions, but this rule allows us to understand what it is supposed to negate)
So, it's a good practice to write "Ovum non sum" or "Non sum ovum", (keeping the "non sum" as a single item)
instead of "Non ovum sum", because I think that the negation is rather on the fact of not-being this thing that being a non-egg (but maybe in other contexts, it would make sense).
The text you reference says "non is usually positioned directly before the word that it negates" (emphasis mine). That means it can be placed elsewhere.
A better way of explaining this is that the "non" modifies the verb "sum" and therefore is placed in front of it
"In Latin, negation can be made simply by placing "nōn" before the main verb."