Would "the young men fight angry" be equivelant or am I confusing my syntax?
No - "angry" is an adjective and modifies "young men". As you wrote the translation it means the young men fought something known as "angry" - and it won't work with the Latin (it would have to at least be in the accusative).
The way DavidBetz put it makes "angry" work as an adverb. Though "irati" is strictly an adjective, it is exceptionally common in Latin to have an adjective describing the subject where in English we often instead use an adverb. I would say it is an acceptable translation.
In English "angry" is not an adverb. In English the adverb would be "angrily".
Adjectival forms like that can function as adverbs as long as they are placed in a sentence in a position where you expect an adverb: "we all left happy", "you did fantastic", "I got it cheap", "I'm feeling bad", and so on.