You can indeed order from REI internationally, we do it all the time. It's one of the easier outdoor shops to deal with from across borders. Only issue with a gift card is that they can only be sent to a US address. Unless you order an E-card, sent via email.
https://www.rei.com/help/placing-int...al-orders.html
Also:
LLBean:
www.llbean.com
Patagonia:
www.patagonia.com
Eddie Bauer:
www.eddiebauer.com
For the above, be sure to use the US site, not the international one. If the US site won't take an international billing address, call customer service to place the order.
(Since US retailers are increasingly using Borderfree for international shipping, some have forgotten that people overseas order for US delivery and haven't tweaked their websites accordingly.)
And a long shot:
Erewhon:
http://www.erehwon.com
They don't ship or bill internationally, but if you find something there that no one else has you could always call customer service and see if they can place an order for you using an overseas billing address.