This is absolutely an ad and you can bet Papa Johns signed off on it. Their Chief Marketing Officer provided quotes. Adexchanger is a site about ads owned by an ad company (Access Intelligence, LLC).

If this ad campaign backfires on them it won't be the first time. They were sued for illegally spamming 500,000 people over text with ads. (https://arstechnica.com/tech-policy/2012/11/papa-johns-faces...). Although ultimately, they got away with paying out just 11 million in cash and a whole lot of coupons for their pizza to a tiny fraction of the people they spammed so maybe it was worth it to them in the end.