Why doesn't the above translate to "Wine with wine"?
If this is an entire sentence, this is clearly a case of two different words that happen to be written the same. [Él/ella] vino [a verb] con vino [a noun]. Hence
"She came with wine"
Here are two more nice examples of the same.
Q: --¿Usted no nada nada?
A: -- Yo no traje traje.
-- You don't swim, do you?
-- I did not bring a swimsuit.
Nada (a verb): you swim
Traje (a verb): I brought
Traje (a noun): a suit
Why does it sound like the conjugation for "Yo" instead of "Él/Ella/Usted"?
Because it is a past tense. The verb "Venir" is very irregular.
It really depends of the context as most of the languages issues, a quote comes to my mind: "Al pan, pan; al vino, vino." (Bread to the bread, wine to the wine) and it means something like keep the things in its place. If you say "vino con vino". I think it can be in some strange context like "Ella mezcló leche con agua y vino con vino." (She mixed milk with water and wine with wine) assuming there where two kinds of wine, maybe, i know it sounds crazy, but it really depends of the context. In spanish we often don't use the pronouns, so again, it will depends of the context becaus "vino" (came) is used with both she and he.
The word "vino" is the third person past of "venir" and for it yo should use: yo vine, tú viniste, usted vino, él/ella vino
Also if you want to use it in a sexual way, as in English (She/He came) you can use it, but you will have to add the pronoun "se" like this "Él/Ella se vino".
"Vino" can mean two unrelated things. A substantive: wine. And a verb, third singular person, past tense of "venir" : (he/she/it) came.
It's just a case of homonyms. English (most languages, I guess) also have them. Examples: "I'll book this book." "Can you pass me that can?"...