As far as I know the "export" feature is simply not available in the "new issue view" yet.
We are working on an app that adds super-powerful PDF export capabilities to Jira Cloud. It integrates to the "new issue view", too (among a lot of other screens):
Find more details here: http://www.midori-global.com/products/better-pdf-exporter-for-jira/cloud/
Thank you for the screenshot, I can see you are using a Next-Gen project. Unfortunately, Next-Gen projects do not currently have the ability to export at the issue level at this time. My suggestion would be to either Create a back up of the entire project and import it as a classic Jira Project into a Jira Cloud instance OR if you just need a few issues you could either clone or move the issue over to a classic Jira project which could then be exported.
I would also feed this back via the feedback button in the lower corner of the navigation panel to the left.
Let me know either way.
Hope this helps :)
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