It's an obstacle to suing Doordash for trademark infringement, which is what you would typically do when someone is doing business in your name without your permission.
Those prohibitions have nothing to do with the original seller asserting his copyright or trademarks or patents, which is what the first sale doctrine prevents. They're just requirements for anyone who is selling food to the public.
To speak more precisely, the first sale doctrines prevent the original seller from asserting intellectual property rights (copyright, patent, trademark) as a basis to prohibit resell. I was writing an internet comment, not a legal brief!
It's an interesting question. I suspect there's some trademark arguments to be made regarding confusion as to who is providing the product and service and whose failures any mistakes reflect. That kind of attribution, and the product quality it promotes, is one of the central purposes of trademark law. But there's also the first sale doctrine--that after you sell your physical product, people can do with it as they please, including resell. I suspect it comes down to how clear Doordash makes it that the restaurant is not involved in the service, but I'm not an expert in these areas, and this is obviously not legal advice.