Is SEO dead for thin sites that deal with affiliate marketing?

Google has made it public in their guidelines that too many affiliate links on a site effects it's rankings significantly.

Does that mean sites that are completely about affiliate marketing (coupons, reviews, etc.) should stop focusing on SEO completely and pursue other channels like PPC?

The problem with PPC for affiliate marketing is that then the merchants (whose affiliate programs you use) prohibit you from driving traffic to them via PPC.

Short answer: not at all.

You can avoid Google penalty by adding rel="nofollow" to your affiliate links or use a URL on your site with a redirect (many sites do that).

You can link to your categories and product pages directly, see this post on getting links without having original content.

Lastly, best link building is the kind that brings you traffic - it doesn't have to be about SEO, if a link is well placed and contextually relevant, it will bring you traffic. So some SEO tactics work for referral traffic building as well.