I had in mind more things like routers, home automation management consoles, etc. which have had web interfaces for a very long time, but it doesn't take all that much power to do it[1], unless you want to run a full Linux kernel and JS and all that other bloat which tiny IoTs don't need.
Indeed. Basic web technologies - client-side HTML, CSS and JavaScript (and I mean writing them directly, not via absurdly wasteful layers of JS frameworks) - are a great tools for adding UIs to connected devices. You don't need that much resources for a HTTP server if you already have TCP/IP connectivity, and you also don't need much resources to output some rudimentary HTML or to process POST requests.
It's also a pretty cool tool for adding UIs to software you code locally. Embedding a HTTP server is simple in most languages, and for some cases, a web interface will be much simpler than building an equivalent from "native" UI components.
--
Incidentally, one of the best demonstrations I saw of that was in the book Land of Lisp. The book teaches you Common Lisp by guiding you through writing a few games. At some point, you end up embedding in your game a very simple HTTP server - and suddenly, you get to have interactive graphics (via SVG) without the author having to teach you lots of stuff about some random UI library.
[1] http://www-ccs.cs.umass.edu/shri/iPic.html (images also mirrored at http://cc2.savs.hcc.edu.tw/~chuavv/smallest/iPic/ipic.html )