I'd say 95% of the apps we build are now based on Unpoly, the rest on React.
We now believe SPAs are not a good default for the type of apps we're building. We're still reaching for SPAs when requirements demand high-frequency user input and optimistic rendering, e.g. for a chat or online game.
Author here. The link is a 6 years old presentation. The demo app has since been rewritten.
The old demo app focused on the downsides of classic multi-page apps (MPAs), i.e. the reason the world moved to SPAs all these years ago. In an MPA clicking a link loses all transient state, like focus, scroll positions and unsaved form state. This can all be solved with updating fragments instead of full pages, while still keeping rendering logic on the server.
Unpoly takes special care to always move the focus to the next relevant element in an interaction. E.g. when a link updates a fragment, the focus is moved to that fragment. Or when an overlay is closed, focus is returned to the link that originally opened that overlay.