Hype is vector based software - right? Does this apply to exporting .oam as vectors to WordPress as well?

You can safely expect the same performance in Wordpress as you do exported as HTML5 on your computer.

No jaggies, no pixels, 100% vector (if you are using the vector, pencil, or shape tools). When you export a oam widget, you’re exporting the full CSS, JS, and HTML that would normally get in a HTML5 export but it is zipped up in a package that is easy to upload to Wordpress as a single file.

So install the plugin, upload the OAM exported from Hype, and give it a go: Tumult Hype Animations Wordpress Plugin … and of course let me know if you have any issues.