After playing around with it on desktop, I have some (feature) requests, I hope you don't mind :)
* is it open source? [EDIT: scratch that, found the source: https://github.com/davidgilbertson/know-it-all ]
* full background coloring of pressed buttons, not just edge
* visual cue as to whether a node has children without having to click on expand
* visual cue of completeness of node's children when collapsed. E.g. I know CSS, but not all of its children. When collapsed, it looks "green".
* Total % counters for each category to help with tracking total goal.
* Description, links to MDN / ... right there in the node somewhere (being open source would help with this a lot, through PRs)
Aside from that, I'm not sure about the usefulness of having buttons on non-leaf nodes, anyway... you'd expect that someone who knows of all a node's leaves knows about the node. I know it's not strictly the same, but is the difference important? It would help simplify the model. Then again I guess that's just personal preference.
Also note that this is very close to a learning system called flashcards. If you added automatic decay and quizzing (you can trust the user to be honest) you get a great way to keep knowledge current. That's the semantic problem with this; I know and will forever know about <base>, but I might soon forget a lot of minutiae I currently happen to know about push notifications because I've been working with them recently. Flashcards take knowledge decay into account.
But again: great stuff! Love it.