@aristotle has it exactly right about what a brand is - it is a "Name, term, design, symbol, or any other feature that identifies one seller's good or service as distinct from those of other sellers."
The OP forgets that the job of a search engine like Google is to return the most RELEVANT search results to a query.
They are not, and never have been designed to rank businesses by which has the most limp-wristed social media consultant.
1-A Twitter account that's more than links from contents from your site where you are involved in a discussion with the public.
Twitter accounts busy with many @replies bore me immensely. Why is this good for a search result?
2-A Facebook Web site with original contents not found on the main site, or contents that offers value added benefits that users would not find on the original Web property - a site that goes beyond just hosting a message board and answering users' questions.
Why would Google reward a site where instead of just having the information on the website, you have to have an account on a third party site and leave to find it there? What has inane social activity got to do with the relevancy of search results to my query?
3-A real distinctive visual identity that can exist outside of the Web.
"Acme's new logo is soooooo last year, down to page two for them!"
4-Apps.
Apps are trendy so they have to be mentioned. I think apples would be just as effective a metric. Whichever site has the most apples wins.
5-A Physical newsletter, or similar contents available as printed material and sold on offline networks.
If this was implemented as a ranking factor by Google the amount of waste paper generated would hasten the planet's deforestation problems.
6-Custom gear, props, with your brand.
I can't wait until Google launches their "Apparel algorithm" and every business brings out a range of t-shirts, ties etc to get ahead in the rankings. Marketing consultants can choose the Autumn range instead of doing real work requiring knowledge.
7-Participation in an industry or a public event like a local festival, not only as a sponsor, but as a guest/speaker.
If this was the case, search results would be a buyable popularity contest. (...)
8-Offline third party recognition, references. For example quotes from a local newspaper on an article where they interviewed you on a specific topic
Google already indexes content from local newspapers that are online. If it's not online, chances are it's not a noteworthy source.
9-An endowment or prize under your property's.
Under your property's what?
10-Mix media contents, like a podcast, a YouTube channel show, or a cable show.
Porpoises would be just as good a metric as podcasts. If you don't have a photo of a porpoise on your homepage, you aren't part of the trendy club and you can't rank in search!