This only applies to Argentines who are residing in Argentina, not foreign residents. And the article seems to only have spoken with Aerolineas Argentina, Austral and a customer of Baquebus. Doesn't seem like a general decree. It seems you can avoid all the paperwork if you go with another airline since you're only required to give these numbers when you purchase tickets with these companies.
Who knows what this government is cooking up now. We'll see. I'd be careful though since usually there are decretos for such policies and as far as I can tell there isn't one out about this yet.
Anyway, just wanted to clarify that this doesn't apply to all residents. Only Argentine citizens.
EDIT:
I don't think this has anything to do with preventing travel. They don't care if Argentines leave. They just don't want the dollars leaving along with them. But yes, IF this is true, and like I said so far there is no evidence that this is state policy enforced by AFIP, then it will affect travel of Argentines. But the goal of the government is not to stop anyone from traveling. They're just panicking about depleting dollar reserves and instead of fixing their own policies, they're punishing the citizens of the country...well, what can I say, you deserve the government you elect.