I'm one of the creators of Godspeed, which is a fast, 100% keyboard oriented to-do app (though we do support drag and drop as well!). And we've got a web app!
Just tried it, and this is very much the opposite of what I am looking for.
What I would like is a very minimal layout. Basically with nothing on the screen. And I want to be able to organize my world by dragging, dropping, swiping recursive items.
https://godspeedapp.com/