> Look at this puzzle. WTF is this?
> The "stretch" ("correct move" according to this tutorial) seems wholly inappropriate compared to 1-point jump, horse-move, diagonal move .... or hell just running in the other direction (to the right, escaping towards the center).
The stretch is good shape here. I can't even tell which keima[0] you have in mind but that makes no sense here. A diagonal also just looks strange, unless you mean hane, which lets opponent cross-cut and will end with losing that stone. Similarly, a 1-point jump (I assume you mean upward) lets opponent wedge in and will end in gote, and running to the right (I assume you mean another 1-point jump) allows opponent to push you around.
The stretch is important here because it prevents opponent's hane, which is very severe. It also threatens to turn and block opponent's expansion decisively, so it may be sente depending on the rest of the board. In general it will make sense to push twice here, then make a one-point jump.
> Or this one is perhaps more egregious. This is simply the wrong direction of play entirely. 20+ point mistake to play the "correct" move here. The correct move is a 2-point jump (or greater) along the 3rd or 4th row northbound.
Per AI, on an empty board, the stretch is about 1 point worse than those jumps (establishing a base); a one-point jump in the same direction of the stretch is about as good as making a base; and best is tenuki. There is simply no urgency to settle those stones without anything else in the area. But stretching or jumping damages Black's shape and limits further expansion of that group. The point is simply to prevent Black's hane there.
Regardless, when they say "correct move", this is not supposed to be about what would be best overall to play in the position. It is supposed to be about a) recognizing the shape and its purpose and b) doing it in a sensible direction. And you really have to learn that sort of thing by example and by physically laying it out, because trying to give the rules for choosing a direction to stretch is harder.
[0] By the way, I'll spot you that Western teachers usually do use English for ikken tobi and kosumi; but "horse-move" is cringe. Most Western players who actually talk about the game will probably know "keima", but you can at least say "knight move".