The Lotte Arai shopping is not particularly extensive. You'll be able to spare your credit card from a partial beating (which it may get from the dining and drinking instead!).
Lotte Arai Ski Shops
The outdoor store adjacent to The Arai sells ski and snowboard accessories such as gloves, beanies, goggles, helmets and après boots, with a small number of items from many brands. Similarly, the shop has some outerwear items from brands such as Northface and Goldwin (a popular Japanese outerwear brand), yet for a reasonably large shop it doesn’t have a lot of stock in it.
The Gelespo shop in the Village Station (gondola base) also stocks various ski and snowboard accessories, so if it's dumping with snow and you need new gloves, goggles or a buff or balaclava, you'll get sorted.
Souvenirs
Lotte Arai has a large souvenir shop that's not heavily stocked. The store sells various Niigata Prefecture products such as sake and other souvenirs. It's rather different to most Japanese ski resort souvenir shops in that it only has upscale keepsakes and there are no cheap and tacky gifts, and you won't find any Hello Kitty paraphernalia!
Grocery Shopping
Other than a handful of vending machines and the expensive sake at the produce store, there isn't anywhere to buy inexpensive drinks or snacks. If you need any groceries or sundries, you'll need to purchase before arrival.