I do not think that this is equivalent, it looks like querying complex JSON objects and not "simple" arrays.

From the "Array Element by Position" example:

  db.blogposts.find( { "comments.0.by" : "Abe" } )

PostgreSQL doesn't have JSON support but it does have XML/Xpath support.

If you stored XML documents in PostgreSQL the similar query to the MongoDB one would be something like this:

  select * from blogposts where (xpath('/comments[0]/@by', doc))::text[] = array['Abe']

Yes it's a little more verbose but not terrible so... at least in my opinion.