I'm not familiar with schema markup; what is it? This article doesn't appear to be a good place to learn about it.
"Schema.org is a markup vocabulary that is standardized and managed as a collaboration of Google and other companies. By working with schema.org, we are creating an open standard, so that the markup you embed can be used by any email product that receives them."[1]
After looking at http://schema.org it alludes to benefiting search engines in parsing structured data. Know any specifics?
Personally, I mark everything I think is meaningful to a human and check that google thinks it is validly formed and how they would display it, but I don't rely on whether they do. With good and consistent metadata, Client side code+CSS can be a bit cleaner and better abstracted and it seems to help a little in the long tail of search engines/aggregators, etc.
One presumes that's google who process it for "other companies" who put it in their pages to be processed by Google.
So basically, Google.
Seems like Bing, Yahoo and Yandex.