1. In many cases it won't be a big enough advantage to win, but in some it will, because there are so many positions where a certain move looks like the best move but it has strong refutation that is very difficult to see (too difficult to see in fact until the game has gotten closer to that position). The discussion was about whether it will ALWAYS be a draw with best play, and my argument shows that's not the case given the assumptions.
2. No, I don't think it means the game is fundamentally flawed. You seem to believe that it SHOULD be a draw with best play, and I think it probably IS a draw with perfect play, but the best engines of today and the best human chess players are so far away from perfect play that whether it is ultimately a draw or not doesn't have much relevance for us.
Anyway, thanks for the discussion. Am off to bed for now.
Analyzing games of engines played against themselves at shallow depths will not get us any closer to determining whether chess is solvable or not.
Engines at large also have nothing to do with solving chess, because solving chess involves presenting a proof and engines are just practical tools for practical purposes and the way they play proves nothing ( it only reflects what humans think about the value of positions, since evaluation functions are programmed into the engines by humans - human guesses coupled with shallow imperfect searches mean nothing in terms of solving chess ).