I ran this through analysis (self analysis) and your numbers appear to be ludicrous. They should probably be + 0.63 and -0.36 which is a huge difference. As far as why it is better I suggest it is a waste of time trying to figure out why, neither you or your opponent would make the moves following the lines or capable on your part to take advantage if your opponent didn't follow the line. Go back if you wish in Analysis and follow them out if you wish.
Position where it was recommended that I move my knight to the rim without immediate recourse
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The first is a re-route forwards. Note the dark square bishop x-rays control of b6 and would be supported by the knight if it could get there. Also, the knight has the option of moving to c5 on the next turn. But if it goes backwards as you moved it, then the queen is obstructed and the knight can only move to the back rank or g2. It is a non active piece and will take to many moves to be active again, as well as un-co-ordinating your pieces in general. It is an exception to the principle of knight on the rim is dim. But look at it this way the big square that the knights work best in runs from c3-f3-f6-c6-c3. Neither positions are optimal but the 4th rank is as central to the flank as the e file is to the files. Just avoid getting the knight trapped or stumbling over themselves and your own pieces.
g3 not g2.
3 hrs ago
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#6
The same Na4 in reply to the b5-b4 Pawn push is found in the Bc4 Fischer-Sozin variation of the Sicilian Najdorf. In that position also, White has a Bishop sitting on e3.
A very similar move - although backed by different ideas entirely - is found in the King's Indian Defense Panno variation.
Here's a position where the engine recommended I move my knight to the edge of the board, rather than back towards the center, in response to my opponent's move b4. Why is moving my knight to the rim considered best in this scenario? (Evaluation if I move it to a4: +.63; Evaluation when I moved it to e2: -.36)