To follow up:
I querried elastic via:
curl -X GET "http://localhost:9200"
curl -X GET "http://server1:9200"
curl -X GET "http://theExtraLongAmazonWebInstanceHostname:9200"
and opened the amazon instance in chrome on :9200.
Result: All of them return the elastic standard message ("You know, for search").
I also tried setting elasticsearch.hosts to the relevant hosts in kibana.yml.
Same result every time.