"where people identify as farmers" means an internal feeling of being a farmer.
"where people identify themselves as farmers" means an external action of declaring themselves to be farmers, like saying they are farmers to someone else.
Here's another example.
"He identified as a police officer." This means he feels like he is a police officer, or he considers himself to be a police officer. For example, a soldier who performs law enforcement duties in a war-torn region may identify as a police officer (consider himself a police officer), even though he is not officially a police officer.
"He identified himself as a police officer." This means he said "I am a police officer!" or he showed his badge to someone.
Here's an example from The Free Dictionary
identify someone as someone
to determine that someone is a certain person.
Can you identify Fred as the perpetrator?
Fred was identified as the thief.
to reveal one's identity or name.
Will you identify the man as Tom?
The stranger identified himself as a meter reader from the gas company.
Notice in both examples there is an object.
"Can you identify Fred as the perpetrator?" 'You' the subject identifies 'Fred' the object as the perpetrator.
"The stranger identified himself as the meter reader." 'The stranger' the subject identified 'himself' the object as the meter reader.
Both of these statements describe external actions.
The sentence the OP has a question about does not have an object.
"An occupational identity where people identify as farmers is emerging..."
There's no object between 'identify' and 'as farmers', therefore that sentence fits most closely with the usual use of the phrase 'identify as'.
As mentioned in Robbie's comment, the use of the phrase 'identify as' is recent, and it's meant to describe a person's internal self-knowledge of his or her gender, regardless of the person's biological sex, or a person's internal self-knowledge of his or her race, regardless of their biological heritage. I'm sure there are other examples in the study of intersectional issues.
So, as I stated, 'identify as' means internal self-knowledge, and 'identify himself as' means an external action declaring one's identity to another. I looked for some kind of reference so I could either confirm or change my answer, but I wasn't able to find one, one way or the other. I think the reason is because this use of the phrase 'identify as' without an object is very recent and it started for the social/political purpose of discussing identity politics.
It's up to you, OP. In my opinion, the writer of the article shouldn't have used 'identify as' in that sentence. He should've used a phrase like 'think of themselves as' (internal self-knowledge) or 'identify themselves as' (external action, people declaring their occupations as farmers to researchers or whomever). The last sentence of the article, "...identity markers are still tied to caste." suggests that internal self-knowledge, what people think of themselves as, is what the writer is discussing.