Also we need another master level game to look at. Here we have Magnus Carlsen the strongest chess player who ever lived vs. GM David Smerdon ranked well over 300 points below Magnus.
Smerdon nevertheless absolutely crushes Carlsen with the Alapin. Being the good team player that he is though Smerdon decided to take a perpetual check draw that would give Australia the victory over Team Norway instead of risking blundering his completely won position into a loss. Here we have it enjoy.
Here's another instructive 5 minute no increment blitz game I played a couple minutes ago.
I've found that Na3! is usually the crushing move in these 2.d5 Alapin's. After Na3 white's development is just too quick to be dealt with especially because white's bishops are free to develop while Black has to play e6 to get his bishop out, and white's dark square bishop develops with a tempo attacking white's queen. Essentially what this Na3 move does is it puts the question of now that the center is wide open how to deal with white's much more rapid piece development, and unfortunately black has no answer.
Your analysis of this game is completely wrong. Black was equal by move five, Na3 is an alright move but it is not "crushing". By move 13 black could have won a piece with 13...Bxa3. This is all backed up by computer analysis.