Maybe there is a misunderstanding between us, but nothing that has changed as far as I know. There was never any way with WordPress to select a “featured video” and my plugin still works as it did. Under the Post Options (what I show in the screenshot previously taken with WordPress 3.5), you select “Replace featured image with video” and insert the URL to your video, which needs to be compatible with WP oEmbed.
If you have a featured image currently set the video will show in its place, and if you don’t the video will still show. So, it realistically has nothing to do with WordPress’s actual concept of selecting a “featured image” —
But on that note anyway, the Media Uploader has been re-designed, but you still configure Featured Images in the same way.