Some key points from the Extension Guidelines:
An extension like you’re suggestion could be considered advertising for the sale of that game.
Your extension idea is exactly that, sending users off-site to purchase a product.
Again, this strictly prohibits what you want to do.
One thing that may still be allowed is if you send the user to an Amazon page selling the item, and if the link is one for the broadcasters Amazon Affiliate (or whatever their program is called) that would allow them to earn revenue from the sale through that link. This runs into the issue though that not all games are sold through Amazon, those that are may not always be the best price so not worth purchasing anyway (Lack of competitive pricing was one of the biggest downfalls of game sales through Twitch), limited options to reach a multi-national audience (Most users will only ever purchase from Amazon using their local site, so linking to the US Amazon site for example wont be useful to potential purchasers in the UK).
TL;DR An extension like you’re suggestion would likely never be allowed for both legal and practicality reasons.