[stumped]

I thought this could not be done, but playing around with a new Lenovo yoga 3 Plus tablet, this worked:
Go to Amazon Web site, select desktop site in browser setings, sign in, play a prime: video.i.e.pkay it in the browser and toggle it to full screen
In chrome there is a pop up to allow giving device properties to Amazon. Or in edge browser there is the same.
Both browsers work .
Video quality quickly builds to be 1080p, confirmed by bottom left indicator, whereas in the prime video app it is sd only.

I am unsure what the exact minimum the prerequisites are. I guess the device needs widevine L1 DRM I dunno if an android os level is also needed. This tablet is at 7.1.
Probably it is necessary to select desktop site in browser, and then have enough CPU power..and the video is then in html5 ?
But I am well pleased , as the only android, not Amazon, tablet I know of that does this out of the box is the £500 Samsung Tab s3,;with the Samsung galaxy prime app.

So I would be interested to know if others can get this to work on non Amazon hardware