Urbandictionary.com says it means:
To rob. Verb. Present tense of juxt.
It has 342 votes but I can't find any evidence of actual usage on a google or COCA search.
The verb to jux as used in New York does mean to rob, for example to rob someone is to jux a head.
Here's a couple of sentences from the book Lush Life by Richard Price where he uses the word jux. Actually the word appears 8 times in the novel. From that it seems to me that it is a "real word" used in NYC.
The answer depends on your definition of "real word".
You gave a word, a definition, and clearly, if it's in the urban dictionary, someone, somewhere is or has used the word with the meaning you described.
My own searching has shown two alternate definitions:
1) short for juxtaposed
2) a word adopted from German (English has a vast tendency to adopt words from other languages) meaning "fun, laughter, joke or jest"
If this is "enough evidence" for it to be a "real word", then it is. If you prefer a different kind of source (like the OED), then it is not a "real word".
Unfortunately, the standard is not agreed upon, which is why sites like Urban dictionary exist: to capture the meanings of some words that aren't in other dictionaries.
It appears jux (to rob) comes from Jamaican Patois jooks (to rob, especially with a pointed weapon), from Carribean jook (to poke) dating back to the early 19th century, and is similar to several west African words meaning to poke, pierce, prick or enter. Jook is now also London gang slang for theft or stabbing.
Ras Dennis Jabari Reynolds' Jabari: Authentic Jamaican Dictionary of the Jamic Language (2006) gives prod and robbery definitions:
A Rasta/Patois Dictionary and Phrases/Proverbs defines jook as:
Partridge (2007) includes:
The OED says jook (also spelled chook, juck, juick and juk) is a Caribbean word meaning to stab, pierce or poke and gives a quotation from H. G. Murray's Tom Kittle's Wake (1877):
And gives an etymology suggesting a west African source:
The Dictionary of the English/Creole of Trinidad & Tobago (2009) includes eight long entries for jook with many citations, with meanings from: to stab; to shove; to wash clothes with a sharp motion against a washboard(a jooking board); a (pelvic) thrust; a cut from a stabbing; a small quick attempt at something to see if you like it; sexual intercourse. The earliest quote is from 1827, for stab:
A jooker is any sharp pointed thing. Jook up is to shove something sharpy; to push severely or repeatedly, to beat up. A jook waist is a sideways hip shift with the ribcage lifted away from the pelvic region, which is sharply pushed outwards. And:
Anita M. Waters' Race, Class, and Political Symbols: Rastafari and Reggae in Jamaican Politics (1985) prints the lyrics of Neville Martin's 1976 election song "The Message" and says:
(Tangentially, Elaine B. Richardson's Hiphop Literacies (2006) notes the roots of jukebox is the jook joint, a place for rowdy dancing, and comes from Wolof dzug and Bambara dzugu meaning to "act disorderly" and "wicked". Richardson also says the Dictionary of Jamaican English (Cassidy and Le Page, 2002) traces it to Fulani jukka (spur, poke; knock down) and Cameroon pidgin (cuk used to mean pierce, prick), noting in one sense it "usually done suddenly", and another is the vulgar usage "to have sexual intercourse (with a woman)".)
A 2005 edition of US urban music Vibe Magazine included a guide to 1995-era slang:
Kermit Ernest Campbell's Gettin' Our Groove On: Rhetoric, Language, And Literacy For The Hip Hop Generation (2005) says:
Herbert C. Covey's Street Gangs Throughout the World (2010) describes a 2002 journalistic account of a street gang from Peckham, London:
Fearless (part of the UK charity, Crimestoppers) says:
It's listed on A lexicon of teen speak by the BBC (2005):
And on the student-authored London Slang Dictionary (2008):
I'm an American, (stated since this question was tagged [american-english] ) and have never heard the word "jux" in any context, so I'd say it's not a "real word". That's not to say that whoever put it in Urban Dictionary made it up. It might be a regionalism, but I have no idea what region that might be.