This is a weird comparison. Electron isn't really a UI framework, it's more of a customized web browser and JS runner, with some platform APIs to bridge the gap. But no, I don't know of anything serious that lets you write web UIs in C++. The closest you'll get are things like Google's Closure Compiler which compile Java to JS.

There's very likely something for C++, but nobody's seriously using that, probably because nobody actually wants this. "All of C++'s hare-brained syntax and slow iteration speed, with none of the performance benefits!" is not a good selling point.

Absolutely, when considering cross-platform UI frameworks in general. In that sense, Qt competes not only with Electron, but also with toolkits like wxWidgets, GTK+, JavaFX, Flash, and some older ones like Java/Swing, Lazarus and Adobe/Macromedia Director.