Question on replacement shipping label from UPS

Even if you modify the label, guess the barcode has the delivery info.

So I was wondering, is it illegal to photoshop JUST the address (not the actual shipment) and have it send to my new place?
Even if it isn't illegal, would they actually deliver it to my new place or will the numbers say that it's supposed to go to my old address?

The correct response (assuming you don't want to bother getting a new label from them) is to contact the local post office where you used to live, as well as where you currently live, and make sure your change of address is still active (if you've never filled out the form for that, you'll need to either ask your postal delivery worker to bring one by for you, or you'll need to go in to the office to fill one out). So long as that is active, USPS is supposed to redirect any mail to the new address without issue. If a service other than USPS is delivering the product, you should be able to manage similar with them- UPS has delivery management through their website, for example.

Given the nature of the product, it'll likely require being signed for upon delivery (confirm with Gamestop on that), so you shouldn't be at risk of any issues if either the company or USPS/UPS makes an error in delivery.

Getting a corrected address label may be a safer and simpler route, however, if you can manage to get it out of them.

http://pe.usps.com/text/dmm100/sending-receiving.htm
https://www.ups.com/content/us/en/resources/sri/ups_my_choice_delivery_instructions.html