Do you need to have the shield plugin to be able to use HTTPS?

I was trying to follow this documentation but, it mentions shield and I was wondering if its needed to be able to have HTTPS on elasticsearch?

Yes you need to have shield to enable HTTPS when following those instructions.

Is there another way to be able to use HTTPS without shield?

Sure, you could put Kibana behind a reverse proxy that exposes an HTTPS interface and connects to Kibana via HTTP.