This match should clearly illustrate that P2 more often has inevitability, while P1 has tempo. Both are extremely exaggerated in this example, 'cause it’s me doing the P1, but that’s the crux, right (as @NikoBolas put it in the original post)? P2 has econ, meaning eventual swing over to bigger and better units or more maxxed heroes and spells making a bigger difference. P1 has first shot at killing heroes/buildings/base, but may struggle to do so, especially as the game progresses.
That said, I do think certain engines/combos (as has been mentioned before) come with some inevitability of their own, and can grant it to Player 1. MoLaC is on everyone’s minds, and Peace Engine, and to a lesser extent Metamorphosis and Earthquake. Playing against those (P1 or P2), the game becomes “Can I shut that down before it shows up and wrecks me sideways?” But then the game gets interesting again when two such strategies are played against each other. When the combos are cheap enough, the econ advantage becomes less relevant (unless someone had to skip tech), the tempo advantage becomes more relevant (unless someone else had to skip tech), and the draws on T3 and T4 become HUGELY relevant.