Yes, KataGo trains entirely through self-play.

It's not "100% pure Zero" in that it doesn't only play entire games from the start. So e.g. it gets supplied with some starting positions that are ones in which some version of KataGo was known to have blindspots (in the hope that this helps it understand those positions better and lose the blindspots) or ones that occur in human games but not in KataGo self-play games (in the hope that this helps it play better against humans and makes it more useful for analysing human games). But I believe all its training is from self-play and e.g. it's never trying to learn to play the same moves as humans did.

(The blindspot-finding is actually pretty clever. What they do is to take a lot of games, and search through them automatically for places where KG doesn't like the move that was actually played but it leads to an outcome that KG thinks is better than what it would have got, and then make a small fraction of KG's training games use those starting positions and also add some bias to the move-selection in those training games to make sure the possibly-better move gets explored enough for KG to learn that it's good if it really is.)

I am not surprised that your concept of local play is less crude than something I explicitly described as the "crudest and most elementary versions". It's not clear to me that we have an actual disagreement here. Isn't there a part of you that winces a little when you have to play an empty triangle, just because it's an ugly very-local configuration of stones?

Here's my (very rough-and-ready; some bits are definitely inaccurate but I don't care because this is just for the sake of high-level intuition) mental model of how a CNN-based go program understands a board position. (This is just about the "static" evaluation and move-proposing; search is layered on top of that and is also very important.)

• There are many layers.
• "Layer zero" knows, for each location on the board, whether there's a stone there and what colour it is. There may also be other "hard-wired" information, like whether any stone there is part of a group that has only one liberty or whether any stone there is part of a group that can be captured in a ladder.
• For each location on the board, each layer is able to look at the previous layer's knowledge at that location and its 8 nearest neighbours. So, e.g., layer 1 might recognize empty triangles, taking that to mean literally "a 2x2 square three of whose points are occupied by stones of one colour, the fourth being empty". Layer 2 might recognize table-shapes and "standard" ko configurations.
• This isn't only about recognizing local combinations of stones, as such. For instance, one thing that might be identified at (say) layer 4 is "a ladder heading northwest from here will collide with an existing stone at distance <= 4, and the first such stone it will reach is white".
• The architecture of the network somewhat encourages later layers to compute some of the same things as earlier ones, only better. So e.g. if there's an "empty triangle unit" on layer 1, there may still be an "empty triangle unit" on layer 5 that computes a more sophisticated notion of empty-triangle-shape-badness that takes into account what other things there are at distance <= 4. (So as you move to later layers you not only recognize larger more complicated patterns of stones, but also refine your understanding of how smaller local shapes are affected by other stuff nearby.)
• KataGo specifically does a thing called "global pooling", which means that e.g. a few layers after it's been able to recognize "there is a ko at this location" it can recognize "there is a ko somewhere on the board" and this information is available everywhere in later layers, so that e.g. it can start attaching more importance to things that might be ko threats.
• The number of layers is sufficiently larger than the size of the board that e.g. the program can figure out "this group is in danger of getting killed unless it makes some better eye shape somewhere around here" even when the group is large enough to span the whole board.
• The things computed in the last layer are then combined to yield predictions of who wins, the final score, what moves are most likely to be good, etc.

So it starts with something similar to those "crudest and most elementary" notions of shape, and gradually refines them to deal with larger and larger scale structures and influence of stones further and further away; after enough layers we're a long way from "duh, empty triangle bad" and into "this group is kinda weak and short of eye-space, and that wall nearby is going to give it trouble, and there's a potential ladder over there that would run through the same area the group needs to run to, so playing here is probably good because in positions like this the resulting fight probably results in a stone here that will break the ladder and make my group over there safer" or "those black stones kinda-enclose some space but it's quite invadable and there's no way he's keeping all of it, especially because we'll get some free moves off that weak black group over there, which will help invade or reduce; it's probably worth about 23 points". (I don't mean to imply that there will be specific numbers the KataGo network computes that have those precise meanings, but that in the sort of position where a pro might think those things there will be things the network does that encode roughly that information.)