How do I fetch a vote given on a node and programmatically apply this vote to the author of the node?
I undesrtand that your question is about a 'code' solution, this one is not but it works, you'll need rules conditional module, and voting rules module , it adds an action: 'a node has been rated', then fecth node-author-by-id, make shure both have the same field (user-bundle and contentype), set user-author-rating-field-value with your node-rating-field-value, or import rule, please edit your field-rating machine name and dependencies as needed. i hope it helps.

    { "rules_set_node_five_star_rate_to_node_author" : {
    "LABEL" : "set node five-star rate to node author",
    "PLUGIN" : "reaction rule",
    "OWNER" : "rules",
    "REQUIRES" : [ "rules", "rules_conditional", "RATING_MODULE_MACHINE_NAME" ],
    "ON" : { "voting_rules_insert_node" : [] },
    "IF" : [
      { "entity_has_field" : { "entity" : [ "node" ], "field" : "field_YOUR_FIVE_STAR_FIELD" } }
    ],
    "DO" : [
      { "entity_fetch" : {
          "USING" : { "type" : "user", "id" : [ "node:author:uid" ] },
          "PROVIDE" : { "entity_fetched" : { "entity_fetched_author_by_id" : "author_by_id" } }
        }
      },
      { "CONDITIONAL" : [
          {
            "IF" : { "entity_has_field" : {
                "entity" : [ "entity-fetched-author-by-id" ],
                "field" : "field_YOUR_FIVE_STAR_FIELD"
              }
            },
            "DO" : [
              { "data_set" : {
                  "data" : [ "entity-fetched-author-by-id:field_YOUR_FIVE_STAR_FIELD" ],
                  "value" : [ "node:field_YOUR_FIVE_STAR_FIELD" ]
                }
              }
            ]
          }
        ]
      }
    ]
  }
}