It makes a lot of sense to improve the performance of email campaigns, but to link poor email reception to Google Search penalties is highly speculative and misguided.
The site in question was most likely affected by the Panda update which was released (in several iterations) around the same time and looking at the articles on the site I can see why this could've happened.
I agree, really hate that restaurants make you download their menu as a .pdf...
Re: "All that said are either of these business types currently reliant on SEO traffic to make a buck?"
I don't think you should look at this as "SEO traffic", but rather ask if it's problem when they are not found through search engines for relevant queries, eg. "brand-name + product-name". Same goes for restaurants, is it a problem if the official site is ranked below a long list of review sites?!
The site in question was most likely affected by the Panda update which was released (in several iterations) around the same time and looking at the articles on the site I can see why this could've happened.