There are a bunch of thread dealing with shipments on this forum. And yes, it's a complicated matter.
If they ship it by a private forwarder like DHL, Fedex or UPS. It goes through Ezeiza and if it gets stuck you have to go there to get it. If they ship it with USPS you will have to go to the national owned state postal office in Retiro (which is a lot better). It really depends on what they label the shipment as.
It's really not true that if you ship it with USPS it will get lost. Sure, the chances of it getting lost is higher. But then again you have to weigh that against the hassle of it getting seized at the airport (having to go all over there and pay extra fines to clear it).
It's always hard to get them to change the shipping label. If it's a game, it's possible you can get them to ship it as an envelope. Although then there is no way for them to know that it was actually successfully received.
Really the best way is to have it shipped to a friend in the States or in Europe and then have them re-ship it here in an envelope. Or alternatively in a package that is labeled as either books or documents with a total value of below 20 USD. Good luck, because when it comes to the custom office in Argentina, it's really what you need.