"The Hungarian tourist is not tall."
Translation:A magyar turista nem magas.
The answer for your question is that in 3rd person (both singular and plural) the conjugated form of the verb 'to be' is omitted. Please note that it not like 'we do not need', but rather 'we must not use' it.
Now, if you'd ask why is this rule - for that I do not know the answer.
No. It's true that "nincs" means "is not", but only in the sense of "does not exist". So you could say "nincs magas magyar turista" to mean "there are no tall hungarian tourists". But for this sentence "nincs" is not appropriate, and there is no other way to say it than with "nem" and the implicit "is".
It wouldn't be a fun language if there are easy-to-grasp rules, no? :)
Hungarian word order is by no means "free", but a lot more flexible than English. Read the comments when you come across longer sentences; there are many examples strewn around.
For this sentence, there's the simple adjective rule: they work just like in English.
- A turista magyar. - The tourist (is) Hungarian. (This is a full sentence.)
- a magyar turista - the Hungarian tourist (This isn't.)
Edit: Okay, you can also interpret "A magyar turista" as a complete sentence: "The Hungarian is a tourist." Point still stands, though.